Skip to main content

Full text of "DTIC ADA138544: Rayleigh-Taylor Instability in the Presence of a Stratified Shear Layer."

See other formats


-fiD-fli38  544  RAVLEIGH-TAVLOR  INSTflBILITV  IN  THE  PRESENCE  OF  fi  1/i 

STRATIFIED  SHEAR  LAVEROJ)  NAVAL  RESEARCH  LAB  WASHINGTON 
DC  P  SATVANARAVANA  ET  AL.  16  FEB  84  NRL-MR-5262 

F/G  4/1 


UNCLASSIFIED 


NL 


AD  A 1 3  8544 


NRL  Memorandum  Report  S263 


Rayleigh-Taylor  Instability  in  the  Presence  of 
a  Stratified  Shear  Layer 

P.  Satyanarayana  and  P  N.  Gi  zdar 

Science  Applications.  Inc. 

McLean.  VA  22102 

J.  D.  Hi;ba  and  S.  L.  Ossakow 

Plasma  Physics  Division 


February  16.  1^84 


This  research  was  sponsored  by  the  Defense  Nuclear  Agency  under  Subtask  S99QMXBC, 
work  unit  00067,  work  unit  title  “Plasma  Structure  Evolution,"  and  by  the  Office  of 
Naval  Research. 


NAVAL  RESEARCH  LABORATORY 
Washington,  D.C. 


OTIC 


s 


lor  I  Uh'i.  r.-kii>e.  tliMrihulien  unlimited 


94-0  3  OZ 


one  FILE  COPY 


SECURITY  CLASSIFICATION  OF  THIS  PAGE 


1*.  REPORT  SECURITY  CLASSIFICATION 

UNCLASSIFIED 


2a  SECURITY  CLASSIFICATION  AUTHORITY 


REPORT  DOCUMENTATION  PAGE 


16  RESTRICTIVE  MARKINGS 


13.  oistrisution/availasility  OF  REFORT 


26-  DECLASSIF »CAT I ON/OOFIN GRADING  SCHEDULE 


4,  FERFORMINC  ORGANIZATION  REFORT  NUMBER(S) 

NRL  Memorandum  Report  5263 


6a  NAME  OF  FERFORMING  ORGANIZATION 

Naval  Research  Laboratory 


6«.  AOORESS  (City.  566  end  ZIP  Codei 


Approved  for  public  release:  distribution  unlimited. 


5.  MONITORING  ORGANIZATION  REPORT  NUMSERIS) 


7a  NAME  OF  MONITORING  ORGANIZATION 


76.  AOORESS  fCify.  Stol#  and  ZIP  Cod*) 


Washington,  DC  20375 


•a  NAME  OF  FUNOINQ/SPONSORING 
ORGANIZATION 

DNA  and  ONR _ 

Sa  AOORESS  (City.  State  and  ZIP  Codet 

Washington,  DC  20305  Arlington,  VA  22217 


11.  TITLE  Unci udo  5mri<y  Clemificeiiom 

(See  page  ii) 


12.  FCRSONAL  AUTMOR(S) 

P.  Satyanarayana,*  P.N.  Guzdar,*  J.D.  Huba  and  S.L.  Ossakow 


13a  TYPE  OP  REPORT 

Interim 


9.  PROCUREMENT  INSTRUMENT  IDENTIFICATION  NUMBER 


10.  SOURCE  OF  FUNOINQ  NOS. 


FROGRAM 
ELEMENT  NO. 


PROJECT 

TASK 

WORK  UNIT 

NO. 

NO. 

NO. 

RR033-02-44 

47-0889-0-4 

474)8834)-! 

IS.  PAGE  COUNT 

59 


Id.  OATS  OF  REPORT  lYr..  Mo..  Dmyt 

February  16,  1984 


IS.  supplementary  notation  -present  address:  Science  Applications,  Inc.,  McLean,  VA  22102 

This  research  was  sponsored  by  the  Defense  Nuclear  Agency  under  Subtask  S99QMXBC,  work  unit  00067,  work  unit  title 


IS.  SUBJECT  TERMS  ^Continue  on  mveree  If  necemary  end  identify  by  block  number > 

Rayleigh-Taylor  instability 

Ionosphere 

Velocity  shear 

Nonlocal  theory 

IS.  ABSTRACT  (Ceelmite  on  mwerae  if  neeeeeery  and  te  stify  by  block  number  1 

>A  nonlocal  theory  of  the  Rayleigh-Taylor  instability  which  includes  the  effect  of  a  transverse  velocity  shear  is  presented. 
A  two  fluid  model  is  used  to  describe  an  inhomogeneous  plasma  under  the  influence  of  gravity  and  sheared  equilibrium  flow 
velocity,  and  to  derive  a  differential  equation  describing  the  generalized  Rayleigh-Taylor  instability.  An  extensive  parametric 
study  is  made  in  the  coilisionless  and  collisional  regime,  and  the  corresponding  dispersion  curves  are  presented.  The  results 
axe  applied  to  the  equatorial  F  region  and  to  barium  releases  in  the  ionosphere. 


2Q  OISTAISUTION/AVAILASIUTY  OS  ABSTRACT  11  ABSTRACT  StCU 

UMCLaSSiRHO/UNLIMITSO  23  SAMS  AS  ART  □  oTlCUSiAsO  UNCLASSIFIED 


Ha  NAM*  OR  AtSRONSlSL*  INDIVIDUAL 

P.  Satyanarayana 


21  ABSTRACT  StCURITY  CLASSIFICATION 


22A  TCLCRMON*  NUMSCR 
I  Include  Aram  Cadet 

(202)  767-3630 


22c  OFFICE  SYMBOL 

Code  4780 


DD  FORM  1473, 83  APR 


EDITION  OF  1  JAN  73  >S  OBSOLETE. 


SECURITY  CLASSIFICATION  OF  THIS  PAGE 


jjCjJWITY  CLAS3I f  ICATION  Of  THIS  PAGE 


11.  TITLE 

RAYLEIGH-TAYLOR  INSTABILITY  IN  THE  PRESENCE  OF  A  STRATIFIED  SHEAR  LAYER 


773T 


5T 


RAYLEIGH-TAYLOR  INSTABILITY  IN  THE  PRESENCE  OF 
A  STRATIFIED  SHEAR  LAYER 

I.  Introduction 

The  Rayleigh-Taylor  instability  (Rayleigh,  1894;  Taylor,  1950)  arises  in 
a  wide  range  of  physical  phenomena.  This  instability  is  primarily  driven  by  a 
gravitational  force  acting  on  an  inverted  density  gradient  (e.g.,  a  heavy 
fluid  supported  by  a  light  fluid).  In  a  magnetized  plasma  these  modes  can 
exist  in  both  the  collisionless  and  colllsional  domains.  For  example, 
theoretical  models  (Hudson  and  Kennel,  1975;  Ossakow,  1979)  and  nui  leal 
simulations  (Scannapieco  and  Ossakow,  1976;  Ossakow  et  al. ,  1979;  Zalesat.  and 
Ossakow,  1980;  Zalesak  et  al.,  1982)  of  the  colllsional  Rayleigh-Taylor 
instability  in  the  earth's  ionosphere  show  that  the  mode  evolves  into  plasma 
bubbles  that  extend  upward  from  the  bottomside  to  the  topside  of  the  F- 
layer.  The  collisionless  interchange  type  instability  (ballooning  mode)  can 
exist  in  the  earth's  plasmasphere  (Vines,  1980)  as  well  as  in  laboratory 
plasmas  (Coppl  and  Rosenbluth,  1966;  Coppi  et  al.,  1979).  These  collisionless 

•  I 

modes  arise  due  to  an  unfavorable  curvature  in  the  magnetic  field  (simulating 
an  effective  gravity)  in  the  presence  of  a  pressure  gradient.  This 
instability  may  also  arise  in  the  acceleration  of  a  heavy  fluid  by  one  of 
lower  density  as  in  targets  accelerated  by  laser  ablation  (Emery  et  al. ,  1982 
and  references  therein)  or  the  deceleration  of  barium  clouds  injected  in  the 
ionosphere  (Pillip,  1971;  Rosenberg,  1971;  Davis  et  al.,  1974;  Fedder,  1980). 

In  some  of  the  above  situations,  the  equilibrium  flow  velocity  is 

observed  to  be  inhomogeneous.  For  example,  in  the  ionosphere,  the  horizontal 

plasma  velocity  during  equatorial  spread  F  (ESF)  reverses  its  direction  as  a 

function  of  altitude  (Kudeki  et  al. ,  1981;  Tsunoda,  1981a;  Tsunoda  and  White, 

1981;  Kelley  et  al.,  1981).  In  the  plasmasphere,  steep  shear  in  the  flow 
Manuscript  approved  November  1,  1983. 


velocity  can  exist  due  to  the  dominating  corotating  electric  field  inside  the 
plasmasphere  and  a  convective  magnetospheric  electric  field  penetrating  across 
the  plasmapause.  This  can  lead  to  a  Kelvin-Helmholtz  type  erosion  of  the 


outer  edge  of  the  plasmasphere  (Vinas,  1980;  Vinas  and  Madden,  1983).  In 
targets  accelerated  by  laser  ablation,  the  Rayleigh-Taylor  instability 
(Bodner,  1974)  nonlinearly  evolves  into  a  bubble  and  spike  structure  (as 
during  ESF)  and  developes  a  strong  shear  in  the  flow  velocity  (Harlow  and 
Welsh,  1966;  Daly,  1967;  Emery  et  al.,  1982).  In  the  absence  of  any  other 
driving  mechanism,  the  velocity  shear  gives  rise  to  a  transverse  Kelvin- 
Helmholtz  instability  in  fluids  (Kelvin,  1910;  Chandrasekhar,  1961)  and  in 
magnetized  plasmas  (Mikhailovskii,  1974).  All  of  the  above  examples  suggest  a 
need  for  a  detailed  study  of  configurations  in  which  the  two  driving 
mechanisms  co-exist,  namely,  inhomogeneous  velocity  flows  and  gravity  (or 
similar  forces). 

The  influence  of  velocity  shear  on  interchange  instabilities  has  been 
studied  by  Drazin  (1958)  and  Chandrasekhar  (1961)  in  the  context  of  fluid 
models;  by  Hamieri  (1979)  in  the  context  of  laboratory  plasmas;  by  Vinas 
(1980)  in  the  context  of  the  plasmasphere;  and  by  Guzdar  et  al.  (1982;  1983) 
in  the  context  of  equatorial  spread  F.  In  this  paper  we  report  on  our 
detailed  study  of  the  Influence  of  velocity  shear  on  the  collisionless  and 
collislonal  Rayleigh-Taylor  instability  and  apply  the  results  to  a  variety  of 
geophysical  phenomena.  We  find  that  the  velocity  shear  can  have  a  dramatic 
effect  on  the  Rayleigh-Taylor  instability  (Guzdar  et  al.,  1982;  1983).  A 
sufficiently  strong  velocity  shear  can  stabilize  the  most  unstable  modes 
(l.e.,  those  for  which  kL  >  1  where  L  is  the  scale  length  of  the  Inhomogeneity 
and  k  is  the  perpendicular  wave  number),  which  leads  to  maximum  growth  in  the 
long  wavelength  regime  (for  which  kL  <  1).  Thus  velocity  shear,  in  some 


domains,  preferentially  excites  a  long  wavelength  mode,  in  sharp  contrast  to 
the  behavior  of  the  mode  in  the  absence  of  velocity  shear. 

This  paper  is  divided  into  five  sections.  In  the  next  section,  we  derive 
the  general  mode  structure  equation  describing  an  inhomogeneous  collisional 
plasma  which  contains  a  sheared  velocity  flow  and  which  is  under  the  action  of 
gravity.  In  the  third  section  we  discuss  the  stability  of  this  plasma  in  two 
limits,  namely,  the  Rayleigh-Taylor  limit  (no  velocity  shear),  and  the  Kelvin- 
Helmholtz  limit  (no  gravity).  In  the  fourth  section  we  present  the  results  of 
the  analysis  of  the  generalized  Rayleigh-Taylor  instability,  i.e.,  when  both 
velocity  shear  and  gravity  are  present.  In  the  final  section,  we  discuss  the 
results  and  apply  them  to  geophysical  phenomena. 


II.  Theory 

We  consider  an  infinite  slab  of  magnetized  plasma.  The  coordinate  system 
is  shown  in  Fig.  1.  The  magnetic  field  is  uniform  and  is  in 

A  A 

the  z_  direction  (B  *  B  z),  the  acceleration  due  to  gravity  is  in  the  x 

A 

direction  (g  *  -g  x),  the  ambient  electric  field  is  inhomogeneous  and  is  in 

A 

the  x  direction  (Eq  -  Eq(x)  x),  and  the  density  is  inhomogeneous  in  the  x 
direction  (n^  ■  n^Cx)).  The  inhomogeneity  in  the  background  electric  field 

A 

leads  to  a  sheared  equilibrium  flow,  Vq(x)  ■  -c  Eq(x)/B  £. 

The  basic  assumptions  used  in  the  analysis  are  as  follows:  (1)  the 
perturbed  quantities  vary  as  5p  ~  5p(x)  exp  [i(k^y  -  tot)],  where  ky  is  the 
wave  number  along  y  direction  and  to  ■  tor  +  iy ,  implying  growth  for  y  >  0; 

(2)  the  ordering  in  the  frequencies  is  such  that  to,  <<  where  v  is 

the  ion-neutral  collision  frequency  and  is  the  ion-gyro-frequency;  (3)  we 
ignore  finite-gyroradius  effects  by  limiting  the  wavelength  domain  to 
kpj<<  1,  where  is  the  mean  ion-Larmot  radius;  (4)  we  neglect  perturbations 
along  the  magnetic  field  (kfl  *  0)  so  that  only  two  dimensional  mode  structure 
in  the  x-y  plane  is  obtained;  (5)  we  retain  ion  inertia  effects,  thereby 
including  the  ion  polarization  drift,  but  Ignore  electron  inertia;  and  (6)  we 
neglect  ion  and  electron  pressure. 

A  key  feature  of  our  analysis  is  that  a  nonlocal  theory  is  developed. 
That  is,  the  mode  structure  of  the  potential  in  the  x  direction,  the  direction 
in  which  density  and  the  flow  velocity  are  assumed  to  vary,  is  determined  by  a 
differential  equation  rather  than  an  algebraic  equation  obtained  by  Fourier 
analysis.  This  technique  allows  one  to  study  modes  which  have  wavelengths 
comparable  to  the  scale  size  of  the  inhomogeneities  (i.e.,  kyL  <  1,  where  L 
represents  scale  lengths  of  the  boundary  layer).  In  fact,  nonlocal  theory  is 


<X 


5 


crucial  to  describe  the  Kelvin-Helmholtz  instability  driven  by  transverse 
velocity  shear  (Milchailovskii,  1974). 

Based  upon  the  assumptions  discussed  above,  the  fundamental  fluid 
equations  used  in  the  analysis  are  continuity  and  momentum  transfer  in  the 
neutfal  frame  of  reference: 

3n 

FT  +  7  *  (na  V  "  °» 

0  -  £  +  I  (2) 

mi(!t  +  li*  7)  li  "  ei  +  |  (li  x  -  Vin  -t  +  mi  4*  (3) 

where  a  denotes  species  (e  for  electrons;  i  for  ions). 

The  equilibrium  velocities  are,  for  electrons 

IeO(x)  5  Vx)  "  (c/8>  Vx)  *  2  »  (*> 

and  for  ions  (to  order  v.  /fl  ) 

in  1 

•  (c/B)  i  [e„  +(B1/e)gJ  »  £  +  (»ln/  Slj) 

+  (!«,)  (ViQ-  7)  Ej 

where  *  eB/m^c  .  The  electrons  simply  _E  x  ]J  drift,  while  the  ions  drift 
with  which  incorporates  the  x  B_  drift,  and  the  effects  of  gravity  and 

the  polarization  electric  field. 

We  substitue  E  -  -  7$  »  -  7  ($o<x)  +  5$)  ,  -  V^Cx)  +  fiV^  , 

n  ■  n^(x)  +  fin  into  Eqs.-  (1)  -  (3).  To  obtain  the  perturbed  velocities  we  do 
not  Fourier  analyze  the  perturbed  quantities  in  the  x  direction  since  the 


equilibrium  quantities  vary  in  that  direction;  we  Fourier  analyze  only  in  the 
y  direction.  Linearizing  Eqs.  (2)  and  (3)  and  making  use  of  Eqs.  (4)  and  (5), 
we  find  the  perturbed  velocities  to  be 


where 


and 


$ «  -  (c/B)  file  6*  x  +  ^  6*  Z], 


s'i 


TT  l'  V*  + 


iil)  -  v 


Q, 


+  (c/B)  [fj  5*  - 


to  +  iv 


in 


a>  «  w  -  kyVQ(x)  and  VQ  -  -  -(c/B)  E^. 

We  substitute  Eqs.  (6)  and  (7)  into  Eq.  (1),  to  obtain 


It  «n  +  i  K Vn  «»  -  It  k  «♦  nn  -  0 


3t  e 


y  0  e  B  y 


(6) 


(7) 


(8) 


It  5ni  *  r??.nof(" ia>  +  vin  +  Vo5  (r? "  ky )  6* 

i  d  X 

+  1  ky  V 

-f  iky  -  Vai>  “8 5* 

-  ra^* 1  “  +  vin  +  1  kyV  no  h  5+  (9> 

+  (8 /at  -  v0)  iy.j  +  <vin/n±)  (g/nr  v0>  fj 

6n. 

+  -si[(g/n,  -  v„)  v;_  +  v,  v:  ]  - 


o 


where  we  have  ignored  terms  of  order  0(oj/0^)  but  have  retained  terms 
proportional  to  and  the  derivatives  of  the  equilibrium  quantities  with 
respect  to  x  (indicated  by  the  primes).  We  now  subtract  the  electron 
continuity  equation,  Eq.  (8),  from  the  ion  continuity  equation,  Eq.  (9),  and 
impose  quasineutrality  (5ng  ■  Sn^).  We  use  Eq.  (8)  to  eliminate  5n^  and 
obtain  the  mode  structure  equation 


a2  a 

— j  <S$  +  p  <5$  +  q  5$  ■  0, 
3x 


(10) 


where 


n'  iv. 

0  ,  in 

p  .  - —  +  — - - 

n0  (  u  +  iv.  )  vin 
In 


Xln  (n0/n0)kyV0  , 

',\)J  ^  ' 


0) 


(11) 


.2  Vro<W  +  V>  .N  *  |« 

q  ■  -  k  +  — ■ —  .  '  ... ....  +  i./ . 

y  “  “  “ 


(M  +lvin) 


<*>(<*>  +  iv±n) 


iv.  k  Vn 
in  y  0 


u>  (a»  +  iv.  )  u) 
in 


t-!-  <W<VV  +  ‘"'o'V  +  <^n/',l„)(n'o/nO)!  <12> 


Note  that  the  solution  of  Eq.  (10)  allows  for  wavepacket  formation 
instead  of  plane  waves.  The  properties  of  the  wavepacket  are  governed  by  the 
coefficients  p  and  q.  From  the  expression  for  q  we  see  that  the  second  term 
involves  the  free  energy  associated  with  the  inhomogeneous  plasma  flow  giving 
rise  to  Kelvin-Helmholtz  instability.  The  third  term  has  the  gravity  and  the 
inverted  density  gradient  leading  to  Rayleigh-Taylor  instability.  The  last 
term  becomes  Important  in  the  moderately  collisional  domain. 


Now  we  define  the  following  dimensionless  parameters  in  order  to  cast  Eq. 
(10)  into  a  dimensionless  form 


,1/2 


<*>  "  a>/(g/L)A/i,  v  -  vin/(g/L)1/2,  VQ  -  V0/(gL)i/Z,  and  k  -  k  L  (13) 


1/2 


where  L  is  the  characteristic  inhomogeneity  scale  length.  We  also  normalize  x 
with  L  and  define  a  new  independent  variable  x  =  x/L.  With  these  definitions, 
Eqs.  (10)-(12)  become 


~2  +  P  lx"  ^  +  3  m  °> 


(14) 


*  %  (nl/n.)  k  V_ 

P  -  (p0/p'J  ♦  1  -S-  [  4 - °-°I - — ], 

ui2  v  (o^ 


(15) 


u>2 


.  -2  +  i  {  jjo  <VV  *  Vi  ,  } 

(Oj  u>2 


-  k  ^  +  (n0Vn0)  +  (no/no)(v'/v)] 

(Oj  o>2 


^  a  a  a 


(16) 


A  A  A  A  A  A  A 

where  toj*  <o  -  k  V^(x)  and  u>2  ■  +  i  v. 

We  use  the  transformation 


5<Kx) 


’Kx)  e 


r 

-J  p(q)  dn 


(17) 


9 


to  write  the  Eq.  (14)  as 


r'  +  q(x)  *  -  o, 


(18) 


where 


Q(x)  ■  q(x)  “  P'(x)/2  -  P(x)2/4.  (19) 

In  solving  the  eigenvalue  problem,  we  use  WKB  boundary  conditions  on  i|> : 

1/4 

ij»  ♦  (1/Q  '  )  exp(-/  Q(n)  dn  )  as  k  +  ±  •  .  (20) 

0 

We  refer  to  Q(x)  as  the  potential  function  and  we  give  the  plots  of  Q(x) 
and  t|;  when  we  solve  Eq.  (18)  numerically  in  the  next  section. 

Equations  similar  to  Eq.  (18)  have  been  obtained  by  several  authors 
studying  the  stability  of  stratified  shear  layers  in  neutral  fluids  (Drazin, 
1958).  However,  usually  a  Rayleigh-Taylor  stable  density  profile  was  chosen, 
mainly  to  examine  the  influence  of  inertia  on  the  velocity  shear  induced 
mixing  phenomenon.  This  situation  differs  slightly  from  the  one  considered  in 
this  paper,  since  we  study  a  situation  where  inverted  density  gradients  and 
velocity  shear  both  are  sources  of  free  energy.  The  collisionless  case  can  be 

A 

compared  with  the  neutral  fluid  case,  and  when  we  set  v  ■  0,  in  Eqs.  (14)-(16) 
we  regain  the  mode  structure  equation  obtained  by  Drazin  (1958).  Drazin 
(1958)  considers  a  weakly  inhomogeneous  plasma,  i.e.,  by  setting  n^/n^  to  zero 
everywhere  except  in  the  driving  term  containing  the  gravity,  and  obtains  a 
simple  equation 


This  implies  that  for  R  <  1/4  the  system  is  stable.  Hamieri  (1979)  considered 
a  more  general  case  applicable  to  a  Tormac  machine  and  arrived  at  a  less 
stringent  condition.  A  theoretical  analysis  in  the  collisionless  and 
collisional  cases  will  be  presented  in  a  future  paper. 


III.  Analysis  and  Results 


The  generalized  mode  structure  equation  [Eq.  (14)]  can  be  better 
understood  by  first  considering  two  limiting  cases:  (A)  the  collisionless  and 
collisional  Rayleigh-Taylor  instability  without  velocity  shear,  and  (B)  the 
Kelvin-Helmholtz  instability  with  no  collisions  or  gravity. 

A.  Rayleigh-Taylor  Instability 

Setting  Vq  ■  0  in  Eq.  (14)  we  obtain 

r'  +  r  -  k2  [i  -  -  0 .  ]  *  -  o  (24) 

a)  (ui  +  iv ) 

Eq.  (24)  can  be  solved  in  the  local  approximation, 

>|>(x)  *  exp(ik^x) ;  k2L2  »  k2L2  »  1  (25) 

and  we  obtain  the  well  known  dispersion  relation  (Haerendel,  1974;  Hudson  and 
Kennel,  1975) 


iv.  (I) 
in 


+  g/L 


(26) 


which  has  the  solution 


CD 


[1  +  (  1  -  48/Vin)]1/2’ 


(27) 


-1  1  0 

where  L  ■  —  ^ —  .  Instability  can  occur  when  g/L„  <  0.  The  collisionless 
n  ng  a x  n 

and  collisional  solutions  are,  respectively, 


•>  -  -  (8/^) 


“  ■  -  1  (*/ln>/vl„ 


v,„  «  12(8/1..)*'  2I, 


uin  »  I2(8/V1/2' 


We  now  solve  Eq.  (24)  numerically  for  a  density  profile 


im 

nQ  -  nQ  exp(-  -^f-)  +  An. 


The  results  are  shown  in  Fig.  2,  which  is  a  plot  of  normalized  growth 
rate,  y  ■  y/(g/L)  ,  vs  normalized  wave  numbers,  k  -  k^L.  Curve  A  is  for 

the  collisionless  Rayleigh-Taylor  instability  and  curve  B  is  for  the 

* 

collislonal  Rayleigh-Taylor  instability  with  v  ■  0.5.  We  use  An/n^  »  0.01  for 

a 

both  cases.  As  expected,  the  growth  rate  maximizes  in  the  regime  k  »  1  and 
the  maximum  growth  rate  agrees  well  with  the  growth  rate  predicted  by  local 

theory  [Eq.  (27)]  with  the  growth  rate  evaluated  at  the  maximum  density 

gradient.  The  potential  function  (Q(x)  given  by  Eq.  (19))  and  the  wave 

A 

function  (iji(x))  »  corresponding  to  k  ■  1.0  are  shown  in  Figs.  3  and  4, 
respectively.  We  note  that  for  An/n^  -  0.01,  n'/n^  has  a  maximum  at 
X  ■  -2.4and  a  potential  well  [-Q(x)  is  a  minimum]  is  formed  around  this  point 
as  can  be  seen  from  Fig.  3.  We  see  from  Fig.  4  that  the  wave  function  also 
localizes  at  x  “  -2.4.  The  negative  sign  implies  that  the  Rayleigh-Taylor 
instability  is  active  where  the  density  gradient  opposes  the  gravity.  We  note 
that  the  wave  function  spreads  out  into  the  positive  region  of  the  x-axls, 
where  the  Rayleigh-Taylor  instability  is  locally  stable  (gravity  acts  in  the 
same  direction  as  the  density  gradient). 


%  •  v*  •_#  *  *  * 


Normalized  growth  rate  Y  =  Y//g /t  vs  k  =  kyL  for  the  Rayleigh- 
Taylor  instability.  Curve  A  represents  the  collisionless 

A 

mode  (v  •  0);  curve  B  represents  the  colllsional  mode 

A  A  ^ 

(v  -  0.5),  where  v  -  v//g/L  .  The  density  profile  used  is  a 
Gaussian-like  profile  nne-*2^^  +  An,  with  An/nQ  ■  0.01. 


B.  Kelvin-Helmholtz  Instability 


We  retain  the  flow  velocity  Vq  ■  Vq(x)  but  consider  a  collisionless, 
uniform  fluid  with  no  gravity.  Eq.  (14)  becomes 


k  V" 

y  o 


Y'  +  [-  k  +  7 — T  „ 
Y  1  y  (oi  -  k^V 


-I  -  0, 


y  0 


(31) 


which  is  well  known  (Mikhailoviskii ,  1974).  Rayleigh's  theorem 

(Mikhailovskii,  1974)  predicts  an  instability  if  the  velocity  profile  has  a 

vanishing  second  derivative  between  the  boundaries,  i.e.,  [92V  /3X2]  *  0, 

u  x0 

where  x^  <  Xq  <  %2  an<^  and  x2  are  c^e  boundaries. 

Equation  (31)  is  solved  for  an  equilibrium  velocity  profile 


Vq  •  VQ  tanh(x/L)  y 


(32) 


and  the  results  are  shown  in  Fig.  5  (curve  A)  in  which  we  plot 

y/(Vq/L  )  versus  kyL.  The  instability  is  purely  growing  and  is  bounded 

between  kyL  *  0  and  1  with  a  maximum  growth  rate  of  y  *  0.18  (Vq/L)  at 

k^L  «  0.45  (Michalke,  1964). 

When  a  density  gradient  is  included,  we  arrive  at  the  following  equation 


*"  +  <no/no)  +  t  “  K 


IV  +  ro  w 
<  “o-  W 


]  \)i  *  0. 


(33) 


Using  the  same  pocedure  as  outlined  following  Eq.  (31),  we  can  show  that 

for  instabilty  the  density  and  velocity  profiles  should  be  such  that 
1  3 

[—  (n0^o  ^x  *  0  where  xq  is  any  point  within  the  boundaries.  It  is 

interesting  to  note  from  Eq.  (33)  that  no  instability  exists  if  the  density 


and  velocity  profiles  are  such  that  9  "^o^O 


Equation  (33)  is 


17 


IV.  Generalized  Xayleigh-Taylor  Instability 


In  the  previous  section  we  considered  the  limiting  cases  where  an 
inverted  density  gradient  in  the  presence  of  gravity  and  a  velocity  shear  | 

individually  give  rise  to  different  instabilities.  We  now  consider  the 
general  problem  where  both  free  energy  sources  jointly  give  rise  to  a 
generalized  Rayleigh-Taylor  instability  (Hamieri,  1979;  Vinas,  1980).  i 

We  consider  two  different  cases:  (A)  a  self-consistent  equilibrium,  and 
(3)  a  general  equilibrium  based  on  the  experimental  observations. 

A.  Self-consistent  Equilibrium  j 

We  choose  the  following  density  profile 

\ 

nQ(x)  -  nQ  (1  +e  tanh(x/L))/(l-e),  (34)  j 

and  the  following  velocity  profile 

I 

V0(x)  -  V0(n0/n0(x))  (35) 


such  that 


‘  V0  "0  -  n0 

0  "  (gL)1/2  V*’  '  *  n0(x)  ’ 

where  we  have  defined  a  dimensionless  parameter  s  =  /(gL)  .  Note  that 

the  zeroth  order  continuity  equation  is  satisfied  by  these  profiles  for 

v.  constant,  i.e., 
in 


[(nn(x)  ]  =  0. 


(36) 


which  implies 


Hq(x)  Eq(x)  *  constant 
or  using  the  definition  of  Vg  from  Eq.  (4), 

ng(x)  V^(x)  =  constant. 

We  solve  Eq.  (14)  numerically  using  these  profiles  and  present  the  results 
below. 

In  Fig.  6  we  plot  the  normalized  growth  rate  v  versus  k  for  the 
collisionless  and  collisional  cases.  The  solid  lines  represent  the 

A 

collisionless  case  (v  *  0)  and  the  dashed  lines  represent  the  collisional  case 

A 

( v  ■  0.5).  We  set  e  *  0.8  in  the  density  profile.  Several  points  are  to  be 
noted  in  this  figure.  First,  we  note  that  in  a  shear-free,  collisionless 
Rayleigh-Taylor  plasma  the  growth  rate  asymptotes  to  the  local  growth  rate 
evaluated  at  the  peak  density  gradient,  (solid  line),  i.e., 

y(lc  »1)  -  [g(n-  /n0)iW  _  .  (37) 

X  =  X 

For  the  density  profile  given  in  Eq.  (36)  n'/nn  maximizes  at  y  obtained  from 


Growth  rate  y  vs  k  for  the  generalized  Rayleigh-Taylor 
instability.  Solid  lines  represent  the  collisionless  case 

A  a 

(v  ■  0.0,  s  =*  0.0,  and  1.0);  dashed  lines  represent  the 

A  A 

collisional  case  (v  =  0.5,  s  ■  0.0,  and  1.0).  The  profiles  used 
are  the  self-consistent  profiles,  Eqs.  (34)  and  (35). 


For  e  =  0.3  Eq.  (33)  yields  ;<  =  “0.55  and  using  this  in  Eq.  (37)  we  find  the 
local  growth  rata  to  be  y  3  1.0.  this  agrees  with  the  growth  rate  for  large 
k  (see  Fig.  6,  solid  line).  Second,  we  find  that  ion-neutral  collisions  have 
a  stabilizing  influence  as  seen  from  the  dashed  line,  which  represents  the 
growth  rate  curve  for  v  =  0.5  and  s  =  0.  Third,  in  a  collisionless  Rayleigh- 


Taylor 

uns  table 

plasma 

,  for  s  =  1.0  (shear 

frequency , 

Vq/L  ,  equal 

to  / g/L) 

velocity 

shear 

stabilizes  the  short 

wavelength 

modes  (solid 

A 

line;  s 

*  1.0);  the 

cut-off 

:  mode  number,  where  the 

growth  rata 

becomes  zero. 

is  k  -  11.0.  As  a  result  the  growth  rate  maximizes  at  k  -  1.5  and  has  a 
c  ° 

maximum  value  y  =  0.675.  Fourth,  in  a  collisional  plasma  also, 

with  v  -  0.5  the  short  wavelength  modes  are  completely  stabilized  (dashed 

line;  s  =  1.0).  The  cut-off  mode  number  in  this  case  is,  k  ~  10.0,  which  is 

c 

less  than  that  of  the  collisionless  case.  The  peak  growth  rate  is  also 

A  A 

smaller  with  y  =  0.  *5  occurring  at  k  =  1.5.  We  see  that  the  ion-neutral 

ul 

collisions  not  only  reduce  the  growth  rate  but  also  reduce  the  cut-off  mode 

number. 

In  Fig.  7  we  give  the  plots  of  the  wavefunction  for  s  =>  0,  k  =  0.5, 

/x 

v  =  0.5  ,  and  s  =  0.3.  We  note  that  the  wavefunction  localizes  at 

Xq  =  -0.55  which  is  the  point  where  the  density  gradient  (n^/n^)  has  an 

extremum.  The  wavefunction  localizes  at  this  point  because  0<x)  has  a  local 

minimum.  We  refer  to  this  point  (for  s  =  0)  as  the  Rayleigh-Tavior 

localization  point.  The  negative  sign  indicates  that  the  density  gradient  has 

to  oppose  the  gravity  for  instability. 

In  Fig.  8  we  give  the  wavefunction  for  the  case  s  *  1  with  the 

same  v,  and  e  as  in  Fig.  7.  The  solid  and  the  dotted  lines  reoresent  the 

in 

real  and  imaginary  parts  of  the  wavefunction,  respectively. 


22 


We  note  that  when 


V ■% 


the  velocity  shear  is  introduced  into  the  problem,  the  wavefunction  picks  up 
an  imaginary  part.  Furthermore,  we  find  that  for  k  >  1,  the  wavefunction 
localizes  at  a  point  closer  to  the  origin  in  the  velocity  shear  layer. 

In  comparing  our  results  with  Drazin  (1958)  we  note  that  since  we  use  a 
density  profile  whose  density  gradient  is  not  a  constant,  and  since  we  have  a 
Raleigh-Taylor  unstable  plasma,  our  threshold  condition  on  R  is  quite 
different.  This  aspect  will  be  dealt  with  in  a  future  paper. 

3.  General  Equilibrium 

Recent  experimental  observations,  made  during  equatorial  spread  F  (ESF) 
(Xudeki  et  al.,  1981)  and  in  the  high  latitude  ionospheric  F  region  (Kelley  et 
al.,  1978),  indicate  that  ionospheric  plasmas  usually  support  inhomogeneous 
equilibrium  plasma  flows.  In  the  case  of  ESF  it  was  found  that  the  flow 
velocity  reverses  its  direction  as  a  function  of  altitude  (x,  the  direction  of 
the  density  gradient).  Furthermore,  the  velocity  reversal  point  moves  up  as 
the  spread  F  develops.  This  equilibrium  situation,  where  the  flow  velocity 
profile  is  not  related  to  the  density  profile  in  a  simple  manner,  is  generated 
by  the  coupling  of  the  plasma  to  the  neutral  atmosphere,  for  example,  by  the 
neutral  winds  and  the  inherent  shear  in  the  neutral  wind  velocity  or  in  the 
case  of  ESF  due  to  an  incomplete  coupling  caused  by  background  ionospheric 
Pedersen  conductivity  away  from  the  equatorial  plane’  (Zalesak  et  al.,  1982). 
Our  earlier  numerical  results  indicate  that  the  inhomogeneity 
in  a)  -  kyVg(x),  and  not  necessarily  the  and  V' ' ,  is  primarily  responsible 
for  stabilizing  the  short  wavelength  interchanger  modes  (Huba  et  al.  ,  1983). 
Therfore,  based  on  the  experimental  observations  (Kudeki  et  al. ,  1981;  Tsunoda 
et  al.,  1981)  and  our  numerical  results  (Huba  et  al.  ,  1983),  we  choose  the 
following  density  and  velocity  profiles  for  a  general  equilibrium  study: 


n0(X)  -  nQ  (1  +  t  tanh  x )  /  ( 1  “  e) 


(39) 


V0(x)  *  Vo  tanh  (x  -  xQ)  (*0) 

where  Xq  is  the  velocity  reversal  point  (in  the  ionospheric  case,  Xq  is  the 
point  where  the  westward  flow  becomes  eastward).  Using  these  profiles  we 
solve  Eq.  (14)  numerically.  Also,  for  simplicity,  we  choose  the  density 
gradient  scale  length  and  velocity  shear  scale  length  to  be  equal.  The 
numerical  results  are  given  below. 

First  we  study  the  role  of  Xq  on  stability  and  determine  the  optimum 
Xq  to  be  used  in  later  calculations.  We  set  v  =  0.5  and  e  *  0.8.  In  Fig.  9 
we  plot  the  normalized  growth  rate  y  versus  k.  Curve  A  shows  the  nonlocal 
collisionless  Rayleigh-Taylor  instability  (s  *  0).  Curves  B,  C,  and  D 
correspond  to  s  *  1  for  different  values  of  Xq*  Curve  B  gives  the  growth 

A 

rates  for  3*1  and  xQ  *  “2.0  which  shows  a  significant  reduction  in  the 

A  A 

growth  rate.  The  growth  rate  maximizes  with  y  *  0.52  at  1:  -  3.0.  However, 
when  Xq  seC  co  "O’ 35  (the  Rayleigh-Taylor  localization  point)  the  growth 
rate  is  sharply  reduced,  maximizing  at  k  ~  0.5  with  y  »  0.256  (curve  C).  For 
Xq  *  0  (curve  D)  there  is  a  significant  reduction  in  the  growth  rate  and  a 
severe  reduction  of  the  k  domain  for  instability.  The  instability  is  bounded 

a  a 

between  k  *  0. 5  and  3.6.  Here,  the  growth  rate  peaks  around  k  ~  1.7. 

For  Xq  *  2.0  (not  shown)  the  growth  rate  curve  is  similar  to  that  of 
Xq  *  -2.0  (curve  C).  From  this  we  conclude  that  the  effects  of  velocity 
shear  are  strongest  when  the  velocity  reversal  point  falls  in  the  Rayleigh- 
Taylor  localization  region. 


26 


'.--•■-'.y-.y VC-. y..---  -V  -w  --v-.  a  -v  »j».- ^ 


-v. 

Vv 


V  *■  Vgtanh(x  *  Xg)  for  Xg*  “0.5,  “2.0,  and  0.0.  Parameters  used 

A  A 

are  s  *  1,  v  ■  0.5,  e  ■  0.8,  and  for  the  profiles  given  in  Eqs. 


In  order  to  throw  some  light  on  the  variation  of  the  dispersion  curves  as 
a  function  of  the  velocity  shear  we  plot  y  versus  k  for  various  values  of 
s  keeping  v,  z ,  and  fixed  at  0.5,  0.3,  and  -0.55,  respectively,  in  Fig. 
10.  This  figure  shows  that  the  general  (non  self-consistent)  profiles  yield 
results  similar  to  those  of  the  self-consistent  profiles  (sec.  IV. A;  see  fig. 
6).  As  s  is  increased,  k^  the  node  number  at  which  the  growth  rate  maximizes, 
moves  towards  smaller  k  and  the  growth  rate  is  substantially  reduced.  For 

a 

very  large  shear,  s  >>  1,  the  mode  becomes  purely  Kelvin-Heimholt?  like, 

preferentially  exciting  a  long  wavelength  mode  (k  ~  0.45  )  with  the  cut-off 

A 

k  less  than  1.0  (to  be  compared  with  Fig.  5).  This  aspect  is  further 

A  A 

illustrated  in  Fig.  11  where  we  plot  Y  versus  s  for  several  values  of 
k.  The  figure  shows  that  for  v  *  0.5  ,  modes  with  k  <  0.3  are  always 
unstable.  Mo  amount  of  shear  (measured  in  units  of  s  )  stabilizes  these 

modes  due  to  the  onset  of  the  Kelvin-Helmholtz  instability  for  these  large  s 


and  small  k.  Furthermore,  for  the  parameters  used  in  the  figure,  moderate  to 

A 

strong  velocity  shear  stabilizes  modes  with  k  >  0.8.  An  empirical  estimate  of 

A  A 

the  shear  that  stabilizes  the  smallest  k  mode  can  be  obtained  from  the  k  = 
0.8  curve  in  Fig.  11,  i.e.,  s  =  2.5  or  Vq/L  ~  2.5  / g/L;  the  figure  also  shows 
that  the  critical  shear  depends  on  the  wavenumber. 

From  Fig.  10  we  see  that  for  v  ■  0.5,  the  mode  with  k  ■  0.45  is  the 

fastest  growing  mode  for  large  s.  It  is  interesting  to  study  the  behavior  of 

A  A  A  ^ 

this  mode  as  a  function  of  s.  In  Fig.  12  we  plot  y  (for  k  *  0.45)  versus  s. 

Curves  A  and  B  represent  the  collisionless  (v  =■  0)  and  collisional 

a  A  A 

(v  *  0.5)  cases  respectively.  Note  that  for  s  *  0,  y  is  purely  Rayleigh- 

A  A 

Taylor-like;  but  as  s  increases,  y  initially  decreases,  which  shows  that 
velocity  shear  is  reducing  the  growth  rate  of  the  Rayleigh-Taylor 

A 

instability.  3eyond  s  >  1  the  velocity  shear  dominates  and  the  Kelvin- 


.n.V.'.'V.^'.V.VA  -.Y.V.v 

•  A_WW«  •_*  4*  •_*  h.  *■  ■  »  .  •»  *  ^ 


28 


M*J 


SWSv 


Study  of  y  versus  s,  for  k  *  0.45  where  the  Kelvin-Helmholtz 

instability  has  maximum  growth  rate.  Curves  A  and  B  refer  to 
* 

y  ■  0.0  and  0.5  respectively. 


Helmholtz  mode  sets  in.  We  note  that  Y  increases  linearly  with  s  for  large  s 


since  it  is  normalized  to  /g/L  and  not  V^/L  .  For  the  collisional  case  we  see 

that  the  velocity  shear  has  a  stronger  influence  over  a  broader  domain  in 

s  and  the  Kelvin-helmoholtz  type  instability  sets  in  for  larger  (s  >  2.5). 

We  see  from  Fig.  10  that  the  cut-off  mode  numbers  and  the  mode  numbers 

where  the  growth  rate  maximizes  vary  significantly  as  a  function  of  velocity 

shear.  In  order  to  show  the  values  they  asymptote  to  for  large  velocity 

shear,  we  plot  the  cut  off  mode  numbers  k  (curves  A),  and  the  mode  numbers  of 

the  fastest  growing  modes,  k  (curves  B)  as  a  function  of  s  in  Fig.  13.  We 

m 

A 

use  Xq  3  -0.55  ,  s  =  0.8,  and  v  =  0  and  0.5.  Solid  lines  represent  the 
collisionless  case  (v  *  0)  and  dashed  lines  represent  the  collisional  case 
(v  *  0.5).  From  the  figure,  we  see  that  k^  ,  and  k^  fall  sharply  as  s  is 

A  A 

increased  and  asymptote  to  smaller  k  values.  For  v  =  0,  (solid  lines) 

A  A  A 

k^  asymptotes  to  0.5  and  k  asymptotes  to  1.0.  3ecause  for  large  s  the  mode 

A  A 

is  Kelvin-Helmholtz-like,  k  and  k  ,as  expected,  attain  the  values  shown  in 

m  c 

A  a  A 

Fig.  5.  For  v  ■  0.5  (dashed  lines)  both  k^  and  kc  are  initially  smaller  than 
those  for  the  collisionless  case.  However,  as  s  is  increased  these  maximum 
and  cut-off  wavenumbers  achieve  a  minimum  value,  then  rise  and  again  asymptote 
to  similar  values  as  those  corresponding  to  the  collisionless  case,  namely  0.5 
and  1.0,  respectively. 

Finally,  in  Fig.  14  we  show  the  effects  of  introducing  a  spatially 
dependent  collision  frequency.  In  the  ionosphere  the  ion-neutral  collision 
frequency  decreases  exponentially  as  a  function  of  the  altitude.  We  use  the 

A 

profile  v  ■  0. 5exp( -x/L) ,  choosing  the  scale  length  to  be  the  same  as  the 
density  gradient  scale  length  for  simplicity.  Curve  A  shows  the  growth  rate 

A  A 

curve  for  constant  collision  frequency,  v  M  0.5,  and  for  s  «  1.0,  and 

A  A 

£  »  0.8.  The  growth  rate  maximizes  at  Y  a  0.256  around  k  =  0.55.  Curve  B, 


with  v  *  v(x),  shows  a  drastic  reduction  in  the  growth  rate.  The  maximum 
growth  rate  (y  *  0.09)  occurs  at  k  ~  0.7.  Interestingly,  in  this  case  the 
lowerbound  of  the  instability  is  shifted.  The  domain  of  unstable  wave  numbers 
is  0.15  <  k  <  1.2;  whereas,  for  the  constant  collision  frequency  case  the 
domain  was  0  <  k  <  1.2  (the  lower  bound  for  curve  A  is  not  shown  in  the 
figure).  Curve  C  for  a  weaker  shear,  namely  s  =*  0.5,  shows  that  the  maximum 
growth  rate  is  comparable  to  that  of  curve  A.  However,  in  this  case  modes 
with  wave  numbers  k  >  3.0  are  completely  stabilized. 


Plots  of  k  (cut-off  mode  numbers)  and  k  (mode  numbers  where 
c  m 

A 

the  growth  rate  maximizes)  as  a  function  of  s  .  The  solid  and 
dashed  lines  correspond  to  the  collisionless  and  collisional 

A 

(v  *  0.5)  cases  respectively.  Curves  A  and  S  refer  to 

A  A 

k  and  k  ,  respectively. 


Figure  14.  Normalized  growth  rate  versus  the  normalized  wavenumbers  for  the 
case  of  a  spatially  dependent  collision  frequency.  The  density 
and  velocity  profiles  are  given  in  Eqs.  (39)  and  (40).  The 

A 

parameters  used  are  s  *  0.8,  Xq  =  -0.55,  and  v  =  0.5.  Curve  A 
refers  to  constant  collision  frequency,  v  =  0.5,  and  s  *  1.0. 

a  A 

Curves  3  and  C  refer  to  v  =  0.5  exp(~x)  and  for  s  =  1.0  and  0.5 
respectively. 


V. 


Discussion  and  Conclusions 


We  have  investigated  the  influence  of  velocity  shear  on  the  Ravleigh- 
Taylor  instability.  The  Ravleign-Taylor  instability  is  driven  by  gravity  and 
an  inverted  density  gradient.  In  general  this  instability  is  most  unstable  in 


the  short  wavelength  domain,  k  L  >  1,  where  L  is  the  density  inhomogeneity 
scale  length  and  k  is  perpendicular  to  the  density  gradient  and  the  magnetic 


field.  We  obtain  the  well  known  results  that  the  maximum  growth  rate  is  given 


by  / g/L  (g/v..  L)  in  the  collisionless  (collisional)  domain.  On  the  other 
hand,  a  sheared  transverse  velocity  drives  the  Kelvin-Heimholtz  instability  in 
the  long  wavelength  domain,  kvL  <  1.  In  the  presense  of  transverse  velocity 
shear,  the  short  wavelength  spectrum  (k  L  >  1)  of  the  Ray leigh-Taylor 
instability  is  strongly  suppressed  or  stabilized  and  the  growth  rate  maximizes 
in  the  long  wavelength  domain  (kvL  <  1).  Thus,  velocity  shear  causes  a  long 
wavelength  mode  to  be  preferentially  excited;  whereas  in  the  absense  of 
velocity  shear  the  dominant  wave  mode  usually  has  a  shorter  wavelength 
determined  by  initial  conditions  or  non-linear  processes.  This  prominant 
conclusion  had  been  stated  in  an  earlier  paper  (Guzdar  et.  al.  ,  1982,  1983). 
We  note  that  the  wavepacket  generally  localizes  in  the  region  where  the 
density  gradient  opposes  the  gravity,  which  in  our  case  also  happens  to  be  the 
shear  layer.  The  wave  function  falls  off  rapidly  away  from  the  localization 
region  of  the  Raleigh-Taylor  instability,  but  still  has  some  finite  amplitude 
in  the  stable  region  (where  _g.7n  is  positive).  This  is  due  to  the  global 
sampling  of  the  entire  density  profile. 

Another  interesting  feature  of  the  generalized  (including  velocity  shear) 
Rayleigh-Taylor  instability  is  its  crucial  dependence  on  the  velocity  reversal 


point.  In  the  absense  of  velocity  shear,  the  wave  function  localizes  at  a 
point,  say  x  >  determined  primarily  by  the  background  density  orofile.  In  the 


case  of  the  hyperbolic  tangent  density  profile  (Eq.  34),  the  wave  function 
localizes  in  the  region  where  the  density  gradient  opposes  the  gravity.  If 
the  velocity  reversal  point,  Xq  (where  the  y-component  of  the  equilibrium 
velocity  changes  sign),  is  in  the  region  where  the  density  gradient  is 
parallel  to  the  gravity,  the  velocity  shear  has  a  generally  stabilizing 
influence  without  the  characteristic  peak  in  the  growth  rate  vs  wave  number 
curve  in  the  long  wavelength  domain  (Fig.  9).  However,  when  xw  “  Xq»  velocity 
shear  reduces  the  growth  rate  significantly  and  moves  the  peak  toward  longer 
wavelengths,  preferentially  exciting  longer  wavelength  modes. 

Two  possible  applications  of  this  theory  to  ionospheric  phenomena  have 
been  discussed  in  a  previous  paper  (Guzdar  et  al.,  1982,  1983).  3riefly,  the 
major  feature  of  this  theory,  viz.,  preferential  excitation  of  a  long 
wavelength  mode,  may  explain  (1)  the  structuring  (1-3  km)  of  barium  releases 
which  are  injected  across  the  magnetic  field  (Linson  et  al.  ,  1980;  Wescott  et 
al.,  1980),  and  (2)  the  long  wavelength  (few  hundred  kms)  oscillations  of  the 
bottomside  F  layer  during  equatorial  spread  F  (Tsunoda  and  White,  1981;  Kelley 
et  al.,  1981). 

The  shaped  barium  release  experiment  (Wescott  et  al. ,  1980)  was  conducted 
at  high  latitudes  in  the  presence  of  a  pulsating  aurora  at  an  altitude  of  571 
km.  Numerical  simulations  showed  that  a  charge  separation  induced  radial 
polarization  electric  field  results  in  an  E.  x  velocity  shear.  This  shear 
layer  seems  to  be  located  in  the  region  where  the  density  gradient  is  steepest 
(Wescott  et  al.,  1980).  Our  analysis  does  not  strictly  apply  in  the  auroral 
environment.  However,  the  basic  instability  leading  to  structuring  of  the 
barium  cloud  is  possibly  a  Rayleigh-Taylor  type  instability  (Pillip,  1971; 
Fedder,  1980)  due  to  the  deceleration  of  the  cloud  (Scholer,  1970).  So  our 
results  in  the  collisionless  domain  could  be  applied  to  this  case.  For 


•  k  ■ 


example,  gradient  scale  sizes  of  500  a  -  1  tan  can  lead  to  irregularity  scale 
sizes  of  1.5  -  3  kms  with  growth  rates  -  10  "  sec  . 

Kudeki  et  al.  (1981)  have  shown,  from  the  observations  at  Jicamarca  using 
a  Radar  interferometer  technique,  that  the  velocity  reversal  point  moves 
upward  as  the  spread-F  structures  evolve.  The  position  of  the  F-peak  was  not 
available  at  the  time  of  these  measurements.  However,  we  conjecture  that 
since  the  velocity  reversal  point  is  at  a  different  location  with  respect  to 
the  F-peak  at  different  times,  the  velocity  shear  induced  long  wavelength 
modulations  of  the  bottom  side  F-layer  may  not  be  apparent  at  all  times,  but 
may  be  seen  when  the  velocity  reversal  point  is  in  the  Rayleigh-Taylor 
localization  region  (namely,  in  the  bottom  side  of  the  F  region). 

Tsunoda  (1983)  recently  has  shown  that  the  background  density  gradient 
has  a  scale  length  of  25  km  when  long  wavelength  fluctuations  were  observed  in 
the  bottom  side  of  the  F-layer.  No  velocity  shear  measurements,  such  as  the 
strength  of  the  shear  or  velocity  reversal  point,  were  available.  We  point 
out  that  the  measured  absense  of  the  velocity  shear  prior  to  or  immediately 
after  the  onset  of  the  wave-like  structure  is  expected  because  ALTAIR  needs 
the  formation  of  the  bubble  and  spike  structures  to  measure  the  plasma 
velocities.  Despite  the  lack  of  shear  data  in  his  paper  there  is  resonable 
agreement  between  the  data  and  the  theoretical  results.  However,  data  on 
velocity  shear,  for  example  by  alternate  techniques,  are  crucial  to  confirm  or 
disprove  the  theory.  The  question  of  short  circuiting  effects  by  the  E-layer, 
raised  by  Tsunoda  (1983),  needs  a  closer  examination  and  is  not  addressed 
here. 

Similar  results  were  obtained  by  Vinas  (1980)  in  connection  with  the 
investigations  of  the  erosion  of  the  plasmapause.  He  conjectured  that  strong 
velocity  shear  could  exist  in  the  plasmapause  region  and  lead  to  long 


38 


wavelength  irregularities  in  competition  with  the  ballooning  mode  type 


interchange  phenomenon.  However,  an  important  difference  exists  in  comparing 
Vinas'  theory  with  ours,  namely,  that  g/L  is  positive  in  his  case,  meaning 
that  the  heavy  fluid  supports  the  lighter  fluid.  We  also  find  similar  results 
in  the  topside  of  the  equatorial  ionosphere,  where  gravity  acts  in  the  same 
direction  as  that  of  the  density  gradient  (a  situation  similar  to  Vinas'  case) 
and  the  collision  frequency  is  very  small.  These  results  indicate  that  in  a 
Rayleigh-Taylor  stable  plasma  the  velocity  shear  could  excite  Kelvin-Helmholtz 
type  modes.  Thus  we  can  conclude  that  in  the  absence  of  equatorial  spread  F 
if  the  flow  velocity  in  the  topside  ionosphere  is  sufficiently  strongly 
inhomogeneous,  it  can  induce  some  large  scale  irregularities.  Figure  5  (curve 


B)  shows  that  if  sufficient  velocity  shear  exists, 
sizes  of  -  300  km  with  weak  growth  rates  (10  s  ) 
the  weakly  collisional  topside  of  the  ionosphere. 

In  conclusion,  we  have  shown  that: 


(i)  Sheared  plasma  velocity  flows  can  have  pronounced  effects  on  the 
collisional  and  collisionless  Rayleigh-Taylor  instabilities. 
Sufficiently  strong  velocity  shear  preferentially  excites  a  long 
wavelength  mode.  This  result  may  explain  the  long  wavelength 
oscillations  of  the  bottomside  F  layer  during  equatorial  spread  F 
and  the  prompt  structuring  of  injected  barium  clouds  (Guzdar  et 
al.,  1982;  1983). 

(ii)  Since  the  wavefunction  localizes  in  the  Rayleigh-Taylor  unstable 
region  we  expect  these  long  wavelength  fluctuations  to  be  seen  at 


the  bottomside  of  the  F-layer 


(iii)  This  phenomenon  is  most  likely  to  occur  when  the  velocity  reversal 
point  is  within  the  Rayleigh-Taylor  localization  region  (where 
gravity  opposes  the  density  gradient). 

(iv)  The  generalized  Rayleigh-Taylor  instability  is  qualitatively 
similar  but  has  quantitatively  different  properties  in  the 
collisional  and  collisionless  domains  (see  fig.  12).  The  cut-off 
mode  numbers  and  maximally  growing  mode  numbers  are  different  in 
these  two  cases  (see  fig.  13). 

(v)  The  properties  of  the  Rayleigh-Taylor  instability  are  similar  for 
self-consistent  as  well  as  for  general  equilibrium  density  and 
velocity  profiles. 

(vi)  As  the  velocity  shear  is  increased,  the  cut-off  mode  numbers  and 
the  maximally  growing  mode  numbers  asymptote  to  values  similar  to 
those  of  the  collisionless  Kelvin-Helmholtz  instability  (see  fig. 
12). 

(vii)  A  spatially  dependent  collision  frequency  alters  the  results 
drastically  by  reducing  the  growth  rate,  and  by  restricting  the 
band  of  unstable  wave  numbers  to  a  smaller  region  (see  fig.  14). 

ACKNOWLEDGMENTS 

This  work  has  been  supported  by  Defence  Nuclear  Agency  and  Office  of 
Naval  Research.  We  thank  P.  Chaturvedi  for  helpful  discussions. 


REFERENCES 


Bodner,  S.E.,  Rayleigh-Taylor  instability  and  laser-pellet  fusion,  Phys.  Rev. 
Lett. ,  33 ,  761,  1974. 

Chandresekhar ,  S.,  Hydrodynamic  and  Hydromagnetic  Stabilility,  Int.  Ser. 

Monographs  on  Physics,  Clarendon  Press,  Oxford,  1961,  p.  494. 

Coppi,  B.,  and  M.N.  Rosenbluth,  Collisional  interchange  instabilities  in  shear 
and  /dl/B  stabilized  systems,  in  Proceedings  of  the  1965  International 
Conference  on  Plasma  Physics  and  controlled  Nuclear  Fusion  Research, 
Paper  CN-21/106,  International  Atomic  Energy  Agency,  Vienna,  1966. 

Coppi,  B.,  J.  Filreis,  and  F.  Pegoraro,  Analytical  representation  and  physics 
of  ballooning  modes,  Ann.  Phys.  (N.Y.)  121,  1,  1979. 

Daly,  B.J.,  Numerical  study  of  two  fluid  Rayleigh-Taylor  instability,  Phys . 
Fluids.,  10,  297,  1967 

Davis,  T.N.,  G.J.  Romick,  E.M.  Wescott,  R.A.  Jeffries,  D.M.  Kerr,  and  H.M. 
Peek,  Observations  of  the  development  of  striations  in  large  barium 
ion  clouds.  Planet.  Space  Sci.,  22,  67,  1974. 

Drazin,  P.G.,  The  stability  of  a  shear  layer  in  an  unbounded  heterogeneous 
inviscid  fluid,  J.  Fluid  Mech.,  4,  214,  1958. 

Emery,  M.H.,  J.H.  Gardner,  and  J.P.  3oris,  The  Rayleigh-Taylor  and  Kelvin- 
Helmholtz  instabilities  in  targets  accelerated  by  laser  ablation,  Phys. 
Rev.  Lett.,  48,  677,  1982. 

Fedder,  J.A.,  Structuring  of  collisionless,  high  velocity  ion  clouds.  Memo 
Rept.  4307,  Nav.  Res.  Lab.,  Washington,  D.C.,  September,  1980.  AD  A089-373 
Fejer,  B.G..  amd  M.C.  Kelley,  Ionospheric  irregularities,  Rev.  Geophys.  Space 
Phys . ,  18,  401,  1980. 


41 


Guzdar,  P.N.,  P.  Satyanarayana,  J.D.  Huba,  and  S.L.  Ossakow,  Influence  of 


velocity  shear  on  Rayleigh-Taylor  instability,  Geophys.  Res.  Lett.,  9_, 
547,  1982. 

Guzdar,  P.N.  ,  P.  Satyanarayana,  J.D.  Huba,  and  S.L.  Ossakow,  Correction  to 
"Influence  of  velocity  shear  on  Rayleigh-Taylor  instability",  Geophys . 
Res.  Lett.,  10,  492,  1983. 

Haerendel,  G.  Theory  of  equatorial  spread  F,  Preprint,  Max-Planck  Institute 
for  Physik  und  Astrophysik,  Garching,  West  Germany,  1974. 

Hameiri,  E.,  Shear  stabilization  of  the  Rayleigh-Taylor  modes,  Phys.  Fluids., 
22,  89,  1979. 

Harlow,  F.H.  and  J.E.  Welch,  Numerical  study  of  large-amplitude  free-surface 
motions,  Phys.  Fluids.,  9_,  842,  1966. 

Huba,  J.D.,  S.L.  Ossakow,  ?.  Satyanarayana,  and  P.N.  Guzdar,  Linear  theory  of 
the  _E  x  instability  with  an  inhomogeneous  electric  field,  J.  Geophys. 
Res. ,  88,  425,  1983. 

Hudson,  M.K. ,  and  C.F.  Kennel,  Linear  theory  of  equatorial  spread  F,  J. 
Geophys.  Res.,  80,  4581,  1975. 

Kelley,  M.C.,  M.F.  Larsen,  C.  LaHoz,  and  J.P.  McClure,  Gravity  wave 

initiation  of  equatorial  spread  F:  A  case  study,  Geophys.  Res., 

J36.9087,  1981. 

Kelvin,  Lord,  Hydrodynamics  and  General  Dynamics,  Cambridge  University  Press, 
Cambridge,  1910,  p.  69 

Kudeki,  E.,  B.G.  Fejer,  D.T.  Farley,  and  H.M.  Ierkic,  Interferometer  studies 
of  equatorial  F  region  irregularities  and  drifts,  Geophys.  Res.  Lett.,  8, 
377,  1981. 

Linson,  L.M.,  and  J.B.  Workman,  Formation  of  striations  in  ionospheric  plasma 
clouds,  J.  Geophys.  Res.,  75,  3211,  1970. 


Michalke,  A.,  On  the  inviscid  instability  of  the  hyperbolic-tangent  velocity 
profile,  J .  Fluid  Mech. ,  19,  543,  1964. 

Mikhailovskii ,  A.B.,  Theory  of  Plasma  Instabilities;  Vol.  II,  Consultants 

3ureau,  New  York,  1974,  p.  141. 

Ossakow,  S.L.  Ionospheric  irregularities,  Rev.  Geophys.  Space  Phys.,  17,  521, 
1979. 

Perkins,  F.W.  and  J.H.  Doles  III,  Velocity  shear  and  the  _E_  x  _B_  instabilty,  J. 
Geophys.  Res.,  80,  211,  1975. 

Phillipp,  W.G.,  Expansion  of  an  ion  cloud  in  the  earth's  magnetic  field.  Planet. 
Space  Sci.,  19,  1095,  1971. 

Rayleigh,  Lord,  Theory  of  Sound,  Dover  Publications,  Inc.,  New  York,  1945. 
Rosenberg,  N.W.,  Observations  of  striation  formation  in  a  barium  ion  cloud,  J . 
Geophys .  Res . ,  76,  6856,  1971. 

Scannapieco,  A.J.  and  S.L.  Ossakow,  Nonlinear  equatorial  spread  F,  Geophys. 
Res.  Lett.,  3,  451,  1976. 

Scannapieco,  A.J.,  S.L.  Ossakow,  S.R.  Goldman,  and  J.M.  Pierre,  Plasma  cloud 
late  time  striation  spectra,  J.  Geophys.  Res.,  81,  6037,  1976. 

Scholer,  M. ,  On  the  motion  of  artificial  ion  clouds  in  the  magnetosphere, 
Planet.  Space  Sci.,  18,  977,  1970. 

Simons,  D.J.,  M.B.  Pongratz,  and  S.P.  Gary,  Prompt  striations  in  ionospheric 
barium  clouds  due  to  a  velocity  space  instability,  J.  Geophys.  Res.,  85, 
671,  1980. 

Taylor,  G.,  The  instability  of  liquid  surfaces  when  accelerated  in  a 
direction  perpendicular  to  their  planes.  I,  Pro,  of  Roy.  Soc.,  (London) 
Ser.  A201,  192,  1950. 

Tsunoda,  R.T.,  Time  evolution  and  dynamics  of  equatorial  backscatter  plumes, 

1.  Growth  phase,  J.  Geophys.  Res.,  86,  139,  1981. 


Tsunoda,  R.T.,  ALTAIR  radar  study  of  equatorial  spread  F,  SRI  International 
Final  Report,  DNA  5689F,  February,  1981.  AD-Al 04-554 

Tsunoda,  R.T.,  R.C.  Livingston,  and  C.L.  Rino,  Evidence  of  a  velocity  shear  in 
bulk  plasma  motion  associated  with  the  post-sunset  rise  of  the  equatorial 
F-layer,  Geophys.  Res.  Lett.,  8_,  807,  1981. 

Tsunoda,  R.T.,  and  B.R.  White,  On  the  generation  and  growth  of  equatorial 
backscatter  plumes-1.  Wave  structure  in  the  bottomside  F  layer,  J. 
Geophys.  Res., 86,  3610,  1981. 

Tsunoda,  R.T.,  On  the  generation  and  growth  of  equatorial  backscatter  plumes- 
2.  Sructuring  of  the  west  walls  of  upwellings,  J.  Geophvs.  Res.,  £ 
4369,  1983. 

Vinas  ,  A.F.,  Magnetohydrodynamic  analysis  of  the  stability  of  the  plasma 
pause,  Ph.D.  thesis,  MIT,  1980. 

v 

Vinas  ,  A.F.  and  T.  Madden,  Shear  flow  balloning  instability  as  a  possible 
mechanism  for  micropulsations  at  the  plasma  pause,  J.  Geophys.  Res., 
(submitted,  1983). 

Wescott,  E.M.,  H.C.  Stenback-Nielsen,  T.J.  Hallinan,  C.S.  Deehr,  G.J.  Romick, 
J.V.  Olson,  J.G.  Roederer,  and  R.  Sydora,  A  high-altitude  barium  radial 
injection  experiment,  Geophys.  Res.  Lett.,  7_,  1037,  1980. 

Zabusky,  N.J.,  J.H.  Doles  III,  and  F.W.  Perkins,  Deformation  and  striation  of 
plasma  clouds  in  the  ionosphere,  2.  Numerical  simulation  of  a  nonlinear 
two-dimensional  model,  J.  Geoohys.  Res.,  78,  711,  1973. 


Si*.  *" 

vy. 

*2 


•.V. 

i 


p 


s-s 


P 

Pv 

»*.■•■. 


rrrrrrr  r  -'.’-V-V-'.  ■  a/  7~ 


,~"l'r.l,.,.'i v v.'yy/vV.^^y^v-: .<,-;a; 


■■.  * 


■  >, 


Zalesak,  S.T.,  and  S.L.  Ossakow,  Nonlinear  equatorial  spread  F:  Spatially 
large  bubbles  resulting  from  large  horizontal  scale  initial  perturbations, 
J.  Geophys.  Res,,  85 ,  2131,  1980. 

Zalesak,  S.T.,  S.L.  Ossakow,  and  ?.K.  Charturvedi,  Nonlinear  equatorial  spread 
F:  The  effect  of  neutral  winds  and  background  Pedersen  conductivity,  J. 

Geophys .  Res ,  87 ,  151,  1982. 


( 


J 


j 


45 


i 


> 


,•  V 


DISTRIBUTION  LIST 


DEPARTMENT  OP  DEFENSE 

ASSISTANT  SECRETARY  OF  DEFENSE 
COMM,  CMD,  CONT  7  INTELL 
WASHINGTON,  D.C.  20201 

DIRECTOR 

COMMAND  CONTROL  TECHNICAL  CENTER 
PENTAGON  RM  3E  685 
WASHINGTON,  D.C.  20301 
OICY  ATTN  C-650 
OICY  ATTN  C-312  R.  MASON 

DIRECTOR 

DEFENSE  ADVANCED  RSCH  PROJ  AGENCY 
ARCHITECT  BUILDING 
1400  WILSON  3LVD. 

ARLINGTON,  VA.  22209 

OICY  ATTN  NUCLEAR  MONITORING  RESEARCH 
OICY  ATTN  STRATEGIC  TECH  OFFICE 

DEFENSE  COMMUNICATION  ENGINEER  CENTER 
1860  WIEHLS  AVENUE 
RESTON,  VA.  22090 
01CY  ATTN  CODE  R410 
01CY  ATTN  CODE  R812 

DEFENSE  TECHNICAL  INFORMATION  CENTER 
CAMERON  STATION 
ALEXANDRIA,  VA.  22314 
02CY 

DIRECTOR 

DEFENSE  NUCLEAR  AGENCY 
WASHINGTON,  D.C.  20305 
OICY  ATTN  STVL 
04CY  ATTN  TITL 
OICY  ATTN  DOST 
03CY  ATTN  RAAE 

COMMANDER 
FIELD  COMMAND 
DEFENSE  NUCLEAR  AGENCY 
KIRTLAND,  AFB,  NM  87115 
OICY  ATTN  FCPR 


DIRECTOR 

INTERSERVICE  NUCLEAR  WEAPONS  SCHOOL 
KIRTLAND  AFB,  NM  37115 

OICY  ATTN  DOCUMENT  CONTROL 

JOINT  CHIEFS  OF  STAFF 
WASHINGTON,  D.C.  20301 

OICY  ATTN  J-3  WWMCCS  EVALUATION  OFFICE 

DIRECTOR 

JOINT  STRAT  TGT  PLANNING  STAFF 
OFFUTT  AF3 
OMAHA,  NB  88113 
01  CT  ATTN  JLTW-2 
OICY  ATTN  JPST  G.  GOETZ 

CHIEF 

LIVERMORE  DIVISION  FLO  COMMAND  DMA 
DEPARTMENT  OF  DEFENSE 
LAWRENCE  LIVERMORE  LABORATORY 
P.O.  SOX  808 
LIVERMORE ,  CA  94550 
OICY  ATTN  FCPRL 

COMMANDANT 

NATO  SCHOOL  (SHAPE) 

APO  SEW  YORK  09172 

OICY  ATTN  U.S.  DOCUMENTS  OFPICER 

UNDER  SECY  OF  DEF  FOR  RSCH  &  ENGRG 
DEPARTMENT  OF  DEFENSE 
WASHINGTON,  D.C.  20301 

OICY  ATTN  STRATEGIC  6  SPACE  SYSTEMS  (OS) 

WWMCCS  SYSTEM  ENGINEERING  ORG 
WASHINGTON,  D.C.  20305 
OICY  ATTN  R.  CRAWFORD 

CO'.DIANDER/ D I  RECTOR 
ATMOSPHERIC  SCIENCES  LABORATORY 
U.S.  .ARMY  ELECTRONICS  COMMAND 
WHITE  SANDS  MISSILE  RANGE,  NM  88002 
OICY  ATTN  DELAS-EO  F.  NILES 


Si 


■5 

■  j 


t 


DIRECTOR 

BMD  ADVANCED  TECH  CTR 
HUNTSVILLE  OFFICE 
P.O.  BOX  1500 
HUNTSVILLE,  AL  35307 

OICY  ATTN  ATC-T  MELVIN  T.  CAPPS 
OICY  ATTN  ATC-0  W.  DAVIES 
01CY  ATTN  ATC-R  DON  RUSS 

PROGRAM  MANAGER 
BMD  PROGRAM  OFFICE 
5001  EISENHOWER  AVENUE 
ALEXANDRIA,  VA  22333 

OICY  ATTN  DACS-3MT  J.  SHEA 

CHIEF  C-E-  SERVICES  DIVISION 
U.S.  ARMY  COMMUNICATIONS  CMD 
PENTAGON  RM  13269 
WASHINGTON,  D.C.  20310 

01CY  ATTN  C-  E-5ERVICES  DIVISION 

COMMANDER 

FRADCOM  TECHNICAL  SUPPORT  ACTIVITY 
DEPARTMENT  0?  THE  ARMY 
FORT  MONMOUTH,  N.J.  07703 

01CY  ATTN  DRSEL-NL-RD  H.  3ENNET 
01CY  ATTN  DRSEL-PL-ENV  a.  30MKE 
01CY  ATTN  J.E.  QUIGLEY 

COMMANDER 

U.S.  ARMY  COMM-ELEC  SNCRG  INSTAL  AGY 
FT.  HUACHUCA,  AZ  35613 

01CY  ATTN  CCC-EMEO  GEORGE  LANE 

COMMANDER 

U.S.  ARMY  FOREIGN  SCIENCE  6  TECH  CTR 
220  7TH  STREET,  NS 
CHARLOTTESVILLE,  VA  22901 
0  ICY  ATTN  DRXST-SD 

COMMANDER 

U.S.  ARMY  MATERIAL  DEV  S  READINESS  CMD 
5001  EISENHOWER  AVENUE 
ALEXANDRIA,  VA  22333 

OICY  ATTN  DRCLDC  J.A.  3ENDER 

COMMANDER 

U.S.  ARMY  NUCLEAR  AND  CHEMICAL  AGENCY 
7500  BACXLICK  ROAD 
BLDG  2073 

SPRINGFIELD,  VA  22150 
OICY  ATTN  LIBRARY 


DIRECTOR 

U.S.  ARMY  3ALLISTIC  RESEARCH  LABORATORY 
ABERDEEN  PROVING  GROUND,  MD  21005 
OICY  ATTN  TECH  LI3RARY  EDWARD  3AICY 

COMMANDER 

U.S.  ARMY  SATCOM  AGENCY 
FT.  MONMOUTH,  NJ  07703 

OICY  ATTN  DOCUMENT  CONTROL 

COMMANDER 

U.S.  ARMY  MISSILE  INTELLIGENCE  AGENCY 
REDSTONE  ARSENAL,  AL  35309 
OICY  ATTN  JIM  G AISLE 

DIRECTOR 

U.S.  ARMY  TRADOC  SYSTEMS  ANALYSIS  AC7IV 
WHITE  SANDS  MISSILE  RANGE ,  NM  88002 
OICY  ATTN  ATAA-5A 
OICY  ATTN  TCC/F.  PAYAN  JR. 

OICY  ATTN  ATTA-TAC  LTC  J.  HESSE 

COMMANDER 

NAVAL  ELECTRONIC  SYSTEMS  COMMAND 
WASHINGTON,  D.C.  20360 

OICY  ATTN  NAVALEX  034  T.  HUCHES 
OICY  ATTN  PME  117 
OICY  ATTN  PME  117-T 
OICY  ATTN  CODE  5011 

COMMANDING  OFFICER 
NAVAL  INTELLIGENCE  SUPPORT  CTR 
4301  SUITLAND  ROAD,  BLDG.  5 
WASHINGTON,  D.C.  20390 

OICY  ATTN  MR.  DUBBIN  STIC  12 

OICY  ATTN  NISC-50 

OICY  ATTN  CODE  5404  J.  GALET 

COMMANDER 

NAVAL  OCCEAN  SYSTEMS  CENTER 
SAN  DIEGO,  CA  92152 
OICY  ATTN  J.  FERGUSON 


NAVAL  RESEARCH  LABORATORY 
WASHINGTON ,  D.C.  "0375 

OICY  ATTN  CODE  4700  S.  L.  Ossakow 

26  CYS  IF  UNCLASS.  1  CY  IF  CLASS) 
01CY  ATTN  COOS  4701  I  Vitkovitsky 
01CY  ATTN  CODE  4780  J.  Huba  (100 
CYS  IF  UNCLASS .  1  CY  IF  CLASS) 
01CY  ATTN  CODE  7500 

01CY  ATTN  CODE  7550 

01CY  ATTN  CODE  7530 

01CY  ATTN  CODS  7551 

01CY  ATTN  CODE  7555 

01CY  ATTN  CODE  4730  E.  MCLEAN 

01CY  ATTN  CODE  4108 

01CY  ATTN  CODE  473C  3.  RIFIN 

20CY  ATTN  CODS  2628 

COMMANDER. 

NAVAL  SEA  SYSTEMS  COMMAND 
WASHINGTON,  D.C.  20362 
01CY  ATTN  CAPT  R.  PITKIN 

COMMANDER 

NAVAL  SPACE  SURVEILLANCE  SYSTEM 
DAHLGREN,  VA  22443 

01CY  ATTN  CAPT  J.H.  BURTON 

OFFICER-IN-CHARGE 
NAVAL  SURFACE  WEAPONS  CENTER 
WHITE  OAK,  SILVER  SPRING,  ND  20910 
01CY  ATTN  CODE  ?31 

DIRECTOR 

STRATEGIC  SYSTEMS  PROJECT  OFFICE 
DEPARTMENT  OF  THE  NAVY 
WASHINGTON,  D.C.  20376 
01CY  ATTN  NSP-2141 
01CY  ATTN  NSSP-2722  FRED  WIMBERLY 

COMMANDER 

NAVAL  SURFACE  WEAPONS  CENTER 
DAHLGREN  LABORATORY 
DAHLGREN,  VA  22448 

OICY  ATTN  CODE  DF-14  R.  3UTLER 

OFFICER  OF  NAVAL  RESEARCH 
ARLINGTON,  VA  22217 
OICY  ATTN  CODE  465 
OICY  ATTN  CODE  461 
OICY  ATTN  CODE  402 
OICY  ATTN  CODE  420 
OICY  ATTN  CODE  421 


COMMANDER 

-AEROSPACE  DEFENSE  CCMMANO/DC 
DEPARTMENT  OF  THE  AIR  FORCE 
ENT  AF3,  CO  S0912 

OICY  ATTN  DC  MR.  LONG 

COMMANDER 

AEROSPACE  DEFENSE  CCMMAND/SPD 
DEPARTMENT  0?  THE  .AIR  FORCE 
ENT  AFB,  CO  80912 
0  ICY  ATTN  XPDQQ 
OICY  ATTN  KP 


AIR  FORCE  GEOPHYSICS  LABORATORY 


HANSCOM 

AF3, 

MA 

01731 

OICY 

ATTN 

OPR 

HAROLD  GARDNER 

OICY 

ATTN 

LX3 

KENNETH  S  •  W .  C; 

OICY 

ATTN 

OPR 

-ALVA  T.  STAIR 

OICY 

ATTN 

PHD 

JURGEN  3UCHA0 

OICY 

ATTN 

PHD 

JOHN  ?.  MULLEN 

-AF  WEAPONS  LABORATORY 
KIRTLAND  AFT,  SM  37117 
OICY  ATTN  SUL 

OICY  ATTN  CA  ARTHUR  H.  GUENTHER 
OICY  ATTN  NTYCE  1LT.  G.  KRAJEI 

AFTAC 

PATRICK  AFB,  FL  32925 
OICY  ATTN  TF/MAJ  WILEY 
OICY  ATTN  TN 

AIR  FORCE  AVIONICS  LABORATORY 
WRIGHT-PATTSSSOH  Ax  3,  OH  45433 
OICY  ATTN  AAD  WADE  HUNT 
OICY  ATTN  .AAD  ALLEN  JOHNSON 

DEPUTY  CHIEF  Or  STAFF 
RESEARCH,  DEVELOPMENT,  6  ACQ 
DEPARTMENT  OF  THE  AIR  FORCE 
WASHINGTON,  D.C.  20330 
OICY  ATTN  AFRDQ 

HEADQUARTERS 

ELECTRONIC  SYSTEMS  DIVISION 
DEPARTMENT  OF  THE  AIR  FORCE 
HANS  COM  -AFB,  MA  01731 
OICY  ATTN  J.  DEA3 

HEADQUARTERS 

ELECTRONIC  SYSTEMS  DIVISICN/Y3EA 
DEPARTMENT  OF  THE  AIR  FORCE 
HANSCOM  .AFB,  MA  01732 
OICY  ATTN  YSEA 


HEADQUARTERS 

ELECTRONIC  SYSTEMS  DIVISICN/DC 
DEPARTMENT  OF  THE  AIR  FORCE 
HANSCOM  AFB,  MA  01731 

01CY  ATTN  DCKC  MAJ  J.C.  CLARK 

COMMANDER 

FOREIGN  TECHNOLOGY  DIVISION,  AFSC 
WRIGHT-? ATTERSON  AF3 ,  OH  45433 
01CY  ATTN  NICD  LI3RARY 

01CY  ATTN  STOP  S.  3 ALLARD 

COMMANDER 

ROME  AIR  DEVELOPMENT  CENTER,  AFSC 
GRIFFI5S  AFB,  NY  13441 

01CY  ATTN  DOC  LI3RARY/TSLD 
01CY  ATTN  OCSE  V.  COYNE 

SAMSO/SZ 

POST  OFFICE  BOX  92960 
WORLDWAY  POSTAL  CENTER 
LOS  ANGELES,  CA  90009 
(SPACE  DEFENSE  SYSTEMS) 

01CY  ATTN  S2J 

STRATEGIC  AIR  COMMAND /XFFS 
OFFUTT  AF3,  NB  63113 

01CY  ATTN  ADWAT2  MAJ  331X3  3AUER 
01CY  ATTN  NRT 

01CY  ATTN  DOK  CHIEF  SCIENTIST 

SAMSO/SK 
P.O.  30X  92960 
WORLDWAY  POSTAL  CENTER 
LOS  ANGELES,  CA  90009 

OICY  ATTN  SKA  (SPACE  COMM  SYSTEMS) 
M.  CLAVIN 

SAMSO/MN 

NORTON  AFB,  CA  92409 
(MIN'JTEMAN) 

0  ICY  ATTN  MNNL 

COMMANDER 

ROME  AIR  DEVELOPMENT  CENTER,  AFSC 
HANSCOM  AF3,  MA  01731 

OICY  ATTN  SEP  A.  LCR3NTCEN 

DEPARTMENT  OF  ENERGY 
LI3RARY  ROOM  C-042 
WASHINGTON,  D.C.  20545 

OICY  ATTN  DOC  CON  FOR  A.  LA30WITZ 


DEPARTMENT  OF  ENERGY 
ALBUQUERQUE  OPERATIONS  OFFICE 
P.O.  30X  5400 
AL3UQUERQUE ,  XM  87115 

OICY  ATTN  DOC  CON  FOR  D.  SHERWOOD 

EGiG,  INC. 

LOS  ALAMOS  DIVISION 

P.O.  30X  809 

LOS  ALAMOS,  NM  35544 

OICY  ATTN  DOC  CON  FOR  J.  BREEDLOVE 

UNIVERSITY  OF  CALIFORNIA 
LAWRENCE  LIVERMORE  LABORATORY 
P.O.  30X  308 
LIVERMORE,  CA  94530 

OICY  ATTN  DOC  COM  FOR  TECH  INFO  DEPT 

OICY  ATTN  DOC  CON  FOR  L-389  R.  OTT 

OICY  ATTN  DOC  CON  FOR  L-31  R.  HAGER 

OICY  ATTN  DOC  CON  FOR  L-46  F.  SEWARD 

LOS  ALAMOS  NATIONAL  LABORATORY 

P.O.  30 X  1663 

LCS  ALAMOS,  NM  87545 

OICY  ATTN  DOC  COM  FOR  J.  WOLCOTT 
OICY  ATTN  DOC  CON  FOR  R.F.  TA3CHEK 
OICY  ATTN  DOC  CON  FOR  E.  JONES 
OICY  ATTN  DOC  CON  FOR  J.  MALIK 
OICY  ATTN  DOC  CON  FOR  R.  JEFFRIES 
OICY  ATTN  DOC  CON  FOR  J.  ZINN 
OICY  ATTN  DOC  CON  FOR  ?.  KEATON 
OICY  ATTN  DCC  CON  FOR  D.  WESTERVELT 
OICY  ATTN  D.  5APPENFIELD 

SANBIA  LABORATORIES 
P.O.  BOX  5800 
ALBUQUERQUE,  NM  87115 

OICY  ATTN  DOC  CON  FOR  W.  BROWN 

OICY  ATTN  DOC  CON  FOR  A.  TH0RN3R0UGH 

OICY  ATTN  DOC  CON  FOR  T.  WRIGHT 

OICY  ATTN  DOC  CON  FOR  D.  DAHLCREN 

OICY  ATTN  DOC  CON  FOR  3141 

OICY  ATTN  DOC  CON  FOR  SPACE  PROJECT  DIV 

SAND l A  LABORATORIES 
LIVERMORE  LABORATORY 
P.O.  30a  969 
LIVERMORE,  CA  94550 

OICY  ATTN  DOC  CON  FOR  3.  MURPHEY 

OICY  ATTN  DOC  CON  FOR  T.  COOK 

OFFICE  OF  MILITARY  APPLICATION 
DEPARTMENT  OF  ENERGY 
WASHINGTON,  D.C.  20545 

OICY  ATTN  DOC  CON  DR.  YO  SONG 


50 


department  of  commerce 

NATIONAL  BUREAU  Or  STANDARDS 
WASHINGTON,  D.C.  20234 

OICY  (ALL  CORRES:  ATTN  SEC  OFFICER  FOR) 

INSTITUTE  FOR  TELECOM  SCIENCES 
NATIONAL  TELECOMMUNICATIONS  a  INTO  .ADMIN 
BOULDER,  CO  S0303 

OICY  ATTN  A.  JEAN  (USCLASS  ONLY) 

OICY  ATTN  W,  UTLAUT 
OICY  ATTN  0.  CR0M3IE 
0 ICY  ATTN  L.  3ERRY 

NATIONAL  OCEANIC  a  ATMOSPHERIC  ADMIN 
ENVIRONMENTAL  RESEARCH  LABORATORIES 
DEPARTMENT  OF  COMMERCE 
30ULDER,  CO  80302 
01CY  ATTN  R.  3 RUB 3 
01CY  ATTN  AERONDMY  LAB  G.  REID 


DEPARTMENT  OF  DEFENSE  CONTRACTORS 


AEROSPACE  CORPORATION 
P.O.  BOX  92937 


LOS  ANG 

ELES, 

CA 

90009 

OICY 

ATTN 

i.  • 

GARF'JXXZL 

OICY 

ATTN 

7  • 

SALMI 

OICY 

ATTN 

V. 

JOSEPHSON 

OICY 

ATTN 

S. 

BOWER 

OICY 

ATTN 

D. 

OLSEN 

ANALYTICAL  SYSTEMS  ENGINEERING  COR? 
5  OLD  CONCORD  ROAD 
BURLINGTON,  MA  01803 

01CY  ATTN  RADIO  SCIENCES 

AUSTIN  RESEARCH  ASSOC.,  INC. 

1901  RUTLAND  DRIVE 
AUSTIN,  TX  73733 

01CY  ATTN  L.  SLOAN 
01CY  A1TN  R.  THOMPSON 

BERKELEY  RESEARCH  ASSOCIATES,  INC. 
P.O.  30X  983 
BERKELEY,  CA  94701 
01CY  ATTN  J.  WORKMAN 
0  ICY  ATTN  C.  PRETTIE 
01CY  ATTN  S.  3RECHT 


P.O.  BOX  3707 
SEATTLE,  VA  93124 


OICY 

ATTN 

•J  0  \L  X  ^  X  2m 

OICY 

ATTN 

D.  MURRAY 

OICY 

ATTN 

G.  HALL 

OICY 

ATTN 

J.  KENNEY 

CHARLES  STAF.K  DRAPER  LABORATORY,  INC. 
555  TECHNOLOGY  SQUARE 
CAMBRIDGE ,  MA  02139 
0 ICY  ATTN  D.3.  COX 
01CY  ATTN  J.?.  GILMORE 

COMSAT  LABORATORIES 
LINTHICUM  ROAD 
CLARKSBURG,  3©  20734 

01CY  ATTN  G.  HYDE 

CORNELL  UNIVERSITY 

DEPARTMENT  OF  ELECTRICAL  ENGINEERING 
ITHACA,  NY  14350 

0 ICY  ATTN  D.T.  FARLEY,  JR. 

ELECTROSPACE  SYSTEMS,  INC. 

30 X  1359 

RICHAPJ3S0N,  TX  7  5030 
0  ICY  ATTN  H.  LOGSTON 
01CY  ATTN  SECURITY  (PAUL  PHILLIPS) 

EOS  TECHNOLOGIES,  INC. 

606  Wilshire  Blvd. 

Santa  Monica,  Calif  90401 
0 1 CY  ATTN  C.B.  GABBARD 

ESL,  INC. 

495  JAVA  DRIVE 
SUNNYVALE,  CA  94086 
0 ICY  ATTN  J.  ROBERTS 
OICY  ATTN  JAMES  MARSHALL 

GENERAL  ELECTRIC  COMPANY 
SPACE  DIVISION 
VALLEY  FORCE  SPACE  CENTER 
GODDARD  3LVD  XING  OF  PRUSSIA 
P.O.  BOX  3555 
PHILADELPHIA,  PA  19101 

OICY  ATTN  M.H.  30RTNER  SPACE  SCI  L.Y3 

GENERAL  ELECTRIC  COMPANY 
P.O.  BOX  1122 
SYRACUSE,  :IY  13201 
OICY  ATTN  F.  REIBERT 


GENERAL  ELECTRIC  TECH  SERVICES  CO.,  INC. 
KMES 

COURT  STREET 
SYRACUSE,  NY  13201 
01CY  ATTN  G.  HILLMAN 

GEOPHYSICAL  INSTITUTE 
UNIVERSITY  0?  ALASKA 
FAIRBANKS,  AX  99701 

(ALL  CLASS  ATTN:  SECURITY  OFFICER) 
OICY  ATTN  T.N.  DAVIS  ('JNCLASS  ONLY) 
01CY  ATTN  TECHNICAL  LIBRARY 
OICY  ATTN  NEAL  BROWN  (UNCLASS  ONLY) 

GTE  SYLVANIA,  INC. 

ELECTRONICS  SYSTEMS  GRP-E ASTERN  DIV 
77  A  STREET 
NEEDHAM,  MA  02194 

OICY  ATTN  DICK  STEINHO? 

HSS,  INC. 

2  ALFRED  CIRCLE 
BEDFORD,  HA  01730 

OICY  ATTN  DONALD  HANSEN 

ILLINOIS,  UNIVERSITY  OF 
107  COBLE  HALL 
150  DAVENPORT  HOUSE 
CHAMPAIGN,  IL  61820 

(ALL  CORRES  ATTN  DAN  MCCLELLAND) 

OICY  ATTN  X.  YEH 

INSTITUTE  FOR  DEFENSE  ANALYSES 
1801  NO.  BEAUREGARD  STREET 
ALEXANDRIA,  VA  22311 
OICY  ATTN  J.M.  AEIN 
OICY  ATTN  ERNEST  BAUER 
OICY  ATTN  HANS  WOLFAPJD 
OICY  ATTN  JOEL  3ENCSTCN 

INTL  TEL  4  TELEGRAPH  CORPORATION 
500  WASHINGTON  AVENUE 
KUTLEY,  NJ  07110 

OICY  ATTN  TECHNICAL  LIBRARY 

JAYCOR 

11011  TORREYANA  ROAD 
P.O.  BOX  35154 
SAN  DIEGO,  CA  92138 

OICY  ATTN  J.L.  SPERLING 


JOHNS  HOPKINS  UNIVERSITY 
APPLIED  PHYSICS  LABORATORY 
JOHNS  HOPKINS  ROAD 
LAUREL,  MD  20810 

OICY  ATTN  DOCUMENT  LIBRARIAN 
OICY  ATTN  THOMAS  POTEMRA 
Old  ATTN  JOHN  DASSOULAS 

KAMAN  SCIENCES  CORP 
P.O.  30X  7463 

COLORADO  SPRINGS,  CO  30933 
OICY  ATTN  T.  MEAGHER 

KAMA.'!  TEMPO-CENTER  FOR  ADVANCED  STUDIES 
816  STATE  STREET  (P.O  DRAWER  QO) 

SANTA  3ARBA3A,  CA  93102 
OICY  ATTN  DAS I AC 
01CT  ATTN  WARREN  S.  KNAPP 
Old  ATTN  WILLIAM  MCNAMARA 
OICY  ATTN  3.  GAMBILL 

LIN"  A3  IT  CORP 
10453  ROSELLE 
SAN  DIEGO,  CA  92121 
Old  ATTN  IRWIN  JAC03S 

LOCKHEED  MISSILES  4  SPACE  CO. ,  INC 
P.O.  BOX  504 
SUNNYVALE,  CA  94038 
OICY  ATTN  DEPT  6C-12 
OICY  ATTN  D.R.  CHURCHILL 

LOCKHEED  MISSILES  4  SPACE  CO.,  INC. 

3251  HANOVER  STREET 
PALO  ALTO,  CA  94304 

OICY  ATTN  MARTIN  WALT  DEPT  52-12 
Old  ATTN  W.L.  IMHO?  DEPT  52-1 
Old  ATTN  RICHARD  G.  JOHNSON  D 
Old  ATTN  J.3.  CLADIS  DF.PT  52-12 

MARTIN  MARIETTA  CORP 
ORLANDO  DIVISION 
P.O.  BOX  5337 
ORLANDO ,  FL  32805 
OICY  ATTN  R.  HEFFNER 

M.I.T.  LINCOLN  LABORATORY 
P.O.  SOX  73 
LEXINGTON,  MA  02173 

OICY  ATTN  DAVID  M.  TOWLE 
OICY  ATTN  L.  LOUGHLIN 
OICY  ATTN  D.  CLARK 


Pi  lO 


MCDONNEL  DOUGLAS  CORPORATION 
5301  30LSA  AVENUE 
HUNTINGTON  3EACH,  CA  92647 
0 ICY  ATTN  N.  HARE. IS 
OICY  ATTN  J.  MO OLE 
OICY  ATTN  GEORGS  MROZ 
OICY  ATTN  Vi.  OLSON 
01CY  ATTN  R.W.  KALPRIN 
01CY  ATTN  TECHNICAL  LIBRARY  SERVICES 

MISSION  RESEARCH  CORPORATION 
735  STATE  STREET 
SANTA  3ARBARA,  CA  93101 
01CY  ATTN  P.  FISCHER 
OICY  ATTN  W.F.  CREVIER 
OICY  ATTN  STEVEN  L.  GUTSC3S 
OICY  ATTN  R.  30GUSCH 
OICY  ATTN  R.  HENDRICK 
OICY  ATTN  RALPH  XIL3 
OICY  ATTN  DAVE  SOWLE 
OICY  ATTN  F.  FAJEN 
OICY  ATTN  M.  SCHEI3E 
OICY  ATTN  CONRAD  L.  LONGMIRS 
OICY  ATTN  3.  WHITE 

MISSION  RESEARCH  CORP. 

1720  RANDOLPH  ROAD.  S.E. 

AL3UQUERQUS ,  NEW  MEXICO  37106 
OICY  R.  STELLINCWERF 
OICY  M.  ALMS 
OICY  L.  WRIGHT 

MITRE  CORPORATION,  THE 
P.O.  30X  208 
3EDFORD,  VIA  01730 

OICY  ATTN  JOHN  MORGANSTSRN 
OICY  ATTN  G.  HARDING 
OICY  ATTN  C.E.  CALLAHAN 

MITRE  CORP 

WESTGATS  RESEARCH  PARK 
1320  DOLLY  :1ADIS0N  BLVD 
MCLEAN,  VA  22101 
OICY  ATTN  W.  HALL 
OICY  ATTN  W.  FOSTER 

PACIFIC-SIERRA  RESEARCH  COR? 

12340  SANTA  MONICA  3 LTD. 

LOS  ANGELES,  CA  90025 

OICY  ATTN  E.C.  FIELD,  JR. 


PENNSYLVANIA  STATE  UNIVERSITY 
IONOSPHERE  RESEARCH  LA 3 
313  ELECTRICAL  ENGINEERING  EAST 
UNIVERSITY  PARK,  PA  16S02 
(NO  CLASS  TO  THIS  ADDRESS) 

OICY  ATTN  IONOSPHERIC  RESEARCH 

PHOTOMETRICS,  INC. 

4  .ARROW  DRIVE 
WOBURN,  MA  01301 

OICY  ATTN  IRVING  L.  XOFSKY 

PHYSICAL  DYNAMICS,  INC. 

P.O.  30X  3027 
BELLEVUE,  WA  98009 

OICY  ATTN  E.J.  FRZMOUW 

PHYSICAL  DYNAMICS,  INC. 

P.O.  30X  10367 
OAKLAND,  CA  94610 
ATTN  A.  THOMSON 

353  ASSOCIATES 
P.O.  3CX  9595 
MARINA  DEL  REY,  CA  90291 
OICY  ATTN  FORREST  GILMORE 
OICY  ATTN  WILLIAM  B.  WRIGHT,  JR 
OICY  ATTN  ROBERT  F.  LELEVIER 
OICY  ATTN  WILLIAM  J.  KARRAS 
OICY  ATTN  H.  ORY 
OICY  ATTN  C.  MACDONALD 
OICY  ATTN  R.  TURCO 
OICY  ATTN  L.  DeRAND 
OICY  ATTN  W.  TSAI 

RAND  CORPORATION,  THE 
1700  MAIN  STREET 
SANTA  MONICA,  CA  90406 
OICY  ATTN  CULLEN  CRAIN 
OICY  ATTN  ED  BEDROZIAN 

RAYTHEON  CO. 

528  BOSTON  POST  ROAD 
SUDBURY,  MA  01776 

OICY  ATTN  BARBARA  ADAMS 

RIVERSIDE  RESEARCH  INSTITUTE 
330  WEST  42nd  STREET 
NEW  YORK,  NT  10036 

OICY  ATTN  VINCE  TRAPANI 


m 

•  ‘j 

■•j 

-  *. 


SCIENCE  APPLICATIONS,  INC. 
1150  PROSPECT  PLATA 
LA  JOLLA,  CA  92037 

OICV  ATTN  LENTS  M.  LINSON 
01CV  ATTN  DANIEL  A.  HAMLIN 
OICV  ATTN  E.  FRIEMAN 
0 ICY  ATTN  E.A.  3TRAXZR 
OICT  ATTN  CURTIS  A.  SMITH 
OICV  ATTN  JACK  MC20UGALL 

SCIENCE  APPLICATIONS,  INC 
1710  CCODRIDGE  DR. 

MCLEAN,  VA  22102 
ATTN:  J.  COCKAYNE 

SRI  INTERNATIONAL 
333  RAVENSVOOD  AVENUE 
MENLO  PARK,  CA  94025 


OICV 

ATTN 

DONALD  MEILSON 

OICV 

ATTN 

ALAN  3 URNS 

OICV 

ATTN 

G.  SMITH 

OICV 

ATTN 

R.  TSUNODA 

Old 

ATTN 

DAVID  A.  JOHNSON 

OICV 

ATTN 

WALTER  G.  CHESSU 

OICV 

ATTN' 

CHARLES  L.  RINO 

OICV 

ATTN 

WALTER  JAVE 

OICV 

ATTN 

J.  VICKREY 

oicv 

ATTN 

RAY  L.  LSADABRANi 

OICV 

ATTN 

C.  CARPENTER 

OICV 

ATTN 

C.  PRICE 

OICV 

ATTN 

R.  LIVINGSTON 

OICV 

ATTN 

V.  GONE ALES 

OICV 

ATTN 

D.  MCDANIEL 

TRW  DEFENSE  i  SPACE  SYS  GROUP 
ONE  SPACE  PARK 
REDONDO  BEACH,  CA  90278 
OICV  ATTN  R.  K.  PLEBCCH 
OICV  ATTN  S.  ALTSCHULER 
OICV  ATTN  D.  DEE 
OICV  ATTN  D /  STOCK., 'ELL 
SSTF/1575 

VTSIDVNE 

SOUTH  3EDF0RD  STREET 
BURLINGTON,  MASS  01303 
OICV  ATTN  W.  REIDV 
OICV  ATTN  J.  CARPENTER 
OICV  ATTN  C.  HUMPHREY 


TECHNOLOGY  INTERNATIONAL  COR? 
7  5  WIGGINS  AVENUE 
BEDFORD,  MA  01730 

OICV  ATTN  W.P.  BOQUIST 

TOYON  RESEARCH  CO. 

P.O.  Sox  5390 
SANTA  3AR3ARA,  CA  93111 
OICV  ATTN  JOHN  ISE,  JR. 
OICV  ATTN  JOEL  GAR3ARIN0 


•'A 


> 


m 

'■i 


9 


9 


■  ~j 

-NJ 


54 


IONOSPHERIC  MODELING  DISTRIBUTION  LIST 
(UNCLASSIFIED  ONLY) 

PLEASE  DISTRIBUTE  ONE  COPY  TO  EACH  OF  THE  FOLLOWING  PEOPLE  (UNLESS  OTHERWISE 
NOTED) 


NAVAL  RESEARCH  LABORATORY 
WASHINGTON,  D.C.  20375 

Dr.  P.  MANGE  -  CODE  4101 
Dr.  P.  GOODMAN  -  CODE  4180 

A.F.  GEOPHYSICS  LABORATORY 
L.G.  HANSCOM  FIELD 
BEDFORD,  MA  01730 
DR.  T.  ELKINS 
DR.  W.  SWIDER 
MRS.  R.  SAGALYN 
DR.  J.M.  FORBES 
DR.  T.J.  KENESHEA 
DR.  W.  BURKE 
DR.  H.  CARLSON 
DR.  J.  JASPERSE 

BOSTON  UNIVERSITY 
DEPARTMENT  OF  ASTRONOMY 
BOSTON,  MA  02215 
DR.  J.  AARONS 

CORNELL  UNIVERSITY 
ITHACA,  NY  14850 
DR.  W.E.  SWARTZ 
DR.  D.  FARLEY 
DR.  M.  KELLEY 

HARVARD  UNIVERSITY 
HARVARD  SQUARE 
CAMBRIDGE,  MA  02138 
dr.  m.b.  Mcelroy 
DR.  R.  LINDZEN 

INSTITUTE  FOR  DEFENSE  ANALYSIS 
400  ARMY/NAVY  DRIVE 
ARLINGTON,  VA  22202 
DR.  E.  BAUER 

MASSACHUSETTS  INSTITUTE  OF 
TECHNOLOGY 
PLASMA  FUSION  CENTER 
LI3RARY,  NW 16-262 
CAMBRIDGE,  MA  02139 


NASA 

GODDARD  SPACE  FLIGHT  CENTER 
GREEN3ELT,  MD  20771 
DR.  K.  MAEDA 
DR.  S.  CURTIS 
DR.  M.  DUBIN 

DR.  N.  MAYNARD  -  CODE  696 
COMMANDER 

NAVAL  AIR  SYSTEMS  COMMAND 
DEPARTMENT  OF  THE  NAVY 
WASHINGTON,  D.C.  20360 
DR.  T.  CZU3A 

COMMANDER 

NAVAL  OCEAN  SYSTEMS  CENTER 
SAN  DIECO,  CA  92152 

MR.  R.  ROSE  -  CODE  5321 

NOAA 

DIRECTOR  OF  SPACE  AND 

ENVIRONMENTAL  LABORATORY 
BOULDER,  CO  80302 
DR.  A.  GLENN  JEAN 
DR.  G.W.  ADAMS 
DR.  D.N.  ANDERSON 
DR.  K.  DAVIES 
DR.  R.F .  DONNELLY 

OFFICE  OF  NAVAL  RESEARCH 
800  NORTH  QUINCY  STREET 
ARLINGTON,  VA  22217 
DR.  C.  JOINER 

PENNSYLVANIA  STATE  UNIVERSITY 
UNIVERSITY  PARK,  PA  16302 
DR.  J.S.  NISBET 
DR.  P.R.  ROHRBAUGH 
DR.  L.A.  CARPENTER 
DR.  M.  LEE 
DR.  R.  DIVANY 
DR.  ?.  BENNETT 
DR.  F.  KLEVANS 

SCIENCE  APPLICATIONS,  INC. 
1150  PROSPECT  PLAZA 
LA  JOLLA,  CA  92037 
DR.  D.A.  U AMLIN 
DR.  E.  FRIEMAN 


STAFFORD  UNIVERSITY 
STANFORD,  CA  94305 
DR.  ?.M.  BANKS 

U.S.  ARM?  ABERDEEN  RESEARCH 
AND  DEVELOPMENT  CENTER 
BALLISTIC  RESEARCH  LABORATORY 
ABERDEEN,  >03 

DR.  J.  HEIMERL 

GEOPHYSICAL  INSTITUTE 
UNIVERSITY  OF  ALASKA 

Fairbanks,  ax  99701 
DR.  L.E.  LEE 

U Nil'S RSITY  OF  CALIFORNIA, 
BERKELEY 

3ERKELEY,  CA  94720 
DR.  M.  HUDSON 

UNIVERSITY  OF  CALIFORNIA 
LOS  ALAMOS  SCIENTIFIC  LABORATORY 
J-10,  MS-664 
LOS  ALAMOS,  XM  37545 
DR.  M.  POSCRATZ 
DR.  D.  SIMONS 
DR.  G.  BARAS CH 
DR.  L.  DUNCAN 
DR.  P.  BERNHARDT 
DR.  5.P.  GARY 

UNIVERSITY  OF  MARYLAND 
COLLEGE  PARK,  MD  20740 
DR.  K.  PAPADOPOULOS 
DR.  S.  OTT 


UNIVERSITY  OF  TEXAS 
AT  DALLAS 

CENTER  FOR  RESEARCH  SCIENCES 
P.O.  BOX  688 
RICHARDSON,  TX  75030 
DR.  R.  HEELIS 
DR.  W.  HANSON 
DR.  J.?.  McCLURE 

UTAH  STATE  UNIVERSITY 
4TH  AND  8TH  STREETS 
LOGAN ,  UTAH  84322 
DR.  R.  KARRIS 
DR.  K.  3 AKER 
DR.  R.  SCHUNK 
DR.  J.  ST. -MAURICE 

PHYSICAL  RESEARCH  LABORATORY 
PLASMA  PHYSICS  PROGRAMME 
AHMEDABAD  380  009 
INDIA 

P.J.  PATHAK,  LIBRARIAN 

LABORATORY  FOR  PLASMA  AND 
FUSION  ENERGY  STUDIES 
UNIVERSITY  OF  MARYLAND 
COLLEGE  PARK,  MD  20742 
JHAN  VARYAN  HELU1AN, 
REFERENCE  LIBRARIAN 


JOHNS  HOPKINS  UNIVERSITY 
APPLIED  PHYSICS  LABORATORY 
JOHNS  HOPKINS  ROAD 
LAUREL,  MD  20310 
DR.  GREENVALD 
DR.  C.  MENG 

UNIVERSITY  OF  PITTSBURGH 
PITTSBURGH,  PA  15213 
DR.  S.  ZABUSKY 
DR.  M.  BIOXOI 
DR.  E.  OVERJ IAN 


56